id	sid	tid	token	lemma	pos
ejpam-6138	1	1	european	european	PROPN
ejpam-6138	1	2	journal	journal	PROPN
ejpam-6138	1	3	of	of	ADP
ejpam-6138	1	4	pure	pure	ADJ
ejpam-6138	1	5	and	and	CCONJ
ejpam-6138	1	6	applied	applied	ADJ
ejpam-6138	1	7	mathematics	mathematic	NOUN
ejpam-6138	1	8	2025	2025	NUM
ejpam-6138	1	9	,	,	PUNCT
ejpam-6138	1	10	vol	vol	NOUN
ejpam-6138	1	11	.	.	PROPN
ejpam-6138	1	12	18	18	NUM
ejpam-6138	1	13	,	,	PUNCT
ejpam-6138	1	14	issue	issue	NOUN
ejpam-6138	1	15	2	2	NUM
ejpam-6138	1	16	,	,	PUNCT
ejpam-6138	1	17	article	article	NOUN
ejpam-6138	1	18	number	number	NOUN
ejpam-6138	1	19	6138	6138	NUM
ejpam-6138	1	20	issn	issn	PROPN
ejpam-6138	1	21	1307	1307	NUM
ejpam-6138	1	22	-	-	SYM
ejpam-6138	1	23	5543	5543	NUM
ejpam-6138	1	24	–	–	PUNCT
ejpam-6138	1	25	ejpam.com	ejpam.com	X
ejpam-6138	1	26	published	publish	VERB
ejpam-6138	1	27	by	by	ADP
ejpam-6138	1	28	new	new	PROPN
ejpam-6138	1	29	york	york	PROPN
ejpam-6138	1	30	business	business	PROPN
ejpam-6138	1	31	global	global	ADJ
ejpam-6138	1	32	on	on	ADP
ejpam-6138	1	33	analysis	analysis	NOUN
ejpam-6138	1	34	of	of	ADP
ejpam-6138	1	35	single	single	ADJ
ejpam-6138	1	36	solution	solution	NOUN
ejpam-6138	1	37	for	for	ADP
ejpam-6138	1	38	a	a	DET
ejpam-6138	1	39	class	class	NOUN
ejpam-6138	1	40	of	of	ADP
ejpam-6138	1	41	bvp	bvp	NOUN
ejpam-6138	1	42	with	with	ADP
ejpam-6138	1	43	generalized	generalized	ADJ
ejpam-6138	1	44	caputo	caputo	PROPN
ejpam-6138	1	45	-	-	PUNCT
ejpam-6138	1	46	katugampola	katugampola	PROPN
ejpam-6138	1	47	fractional	fractional	ADJ
ejpam-6138	1	48	derivative	derivative	ADJ
ejpam-6138	1	49	zouaoui	zouaoui	NOUN
ejpam-6138	1	50	bekri	bekri	PROPN
ejpam-6138	1	51	1,2	1,2	NUM
ejpam-6138	1	52	,	,	PUNCT
ejpam-6138	1	53	mohammad	mohammad	PROPN
ejpam-6138	1	54	esmael	esmael	PROPN
ejpam-6138	1	55	samei	samei	PROPN
ejpam-6138	1	56	3	3	NUM
ejpam-6138	1	57	,	,	PUNCT
ejpam-6138	1	58	vedat	vedat	PROPN
ejpam-6138	1	59	suat	suat	PROPN
ejpam-6138	1	60	erturk	erturk	PROPN
ejpam-6138	1	61	4	4	NUM
ejpam-6138	1	62	,	,	PUNCT
ejpam-6138	1	63	salma	salma	PROPN
ejpam-6138	1	64	haque	haque	PROPN
ejpam-6138	1	65	5	5	NUM
ejpam-6138	1	66	,	,	PUNCT
ejpam-6138	1	67	nabil	nabil	PROPN
ejpam-6138	1	68	mlaiki	mlaiki	PROPN
ejpam-6138	1	69	5,∗	5,∗	NUM
ejpam-6138	1	70	1	1	NUM
ejpam-6138	1	71	laboratory	laboratory	NOUN
ejpam-6138	1	72	of	of	ADP
ejpam-6138	1	73	fundamental	fundamental	ADJ
ejpam-6138	1	74	and	and	CCONJ
ejpam-6138	1	75	applied	applied	ADJ
ejpam-6138	1	76	mathematics	mathematic	NOUN
ejpam-6138	1	77	,	,	PUNCT
ejpam-6138	1	78	university	university	NOUN
ejpam-6138	1	79	of	of	ADP
ejpam-6138	1	80	oran	oran	ADJ
ejpam-6138	1	81	1	1	NUM
ejpam-6138	1	82	,	,	PUNCT
ejpam-6138	1	83	ahmed	ahmed	PROPN
ejpam-6138	1	84	ben	ben	PROPN
ejpam-6138	1	85	bella	bella	PROPN
ejpam-6138	1	86	,	,	PUNCT
ejpam-6138	1	87	es	es	NOUN
ejpam-6138	1	88	-	-	PUNCT
ejpam-6138	1	89	senia	senia	NOUN
ejpam-6138	1	90	,	,	PUNCT
ejpam-6138	1	91	31000	31000	NUM
ejpam-6138	1	92	oran	oran	NOUN
ejpam-6138	1	93	,	,	PUNCT
ejpam-6138	1	94	algeria	algeria	PROPN
ejpam-6138	1	95	2	2	NUM
ejpam-6138	1	96	department	department	NOUN
ejpam-6138	1	97	of	of	ADP
ejpam-6138	1	98	sciences	science	NOUN
ejpam-6138	1	99	and	and	CCONJ
ejpam-6138	1	100	technology	technology	NOUN
ejpam-6138	1	101	,	,	PUNCT
ejpam-6138	1	102	institute	institute	NOUN
ejpam-6138	1	103	of	of	ADP
ejpam-6138	1	104	sciences	sciences	PROPN
ejpam-6138	1	105	,	,	PUNCT
ejpam-6138	1	106	nour	nour	PROPN
ejpam-6138	1	107	-	-	PUNCT
ejpam-6138	1	108	bachir	bachir	PROPN
ejpam-6138	1	109	university	university	NOUN
ejpam-6138	1	110	center	center	NOUN
ejpam-6138	1	111	,	,	PUNCT
ejpam-6138	1	112	el	el	NOUN
ejpam-6138	1	113	-	-	NOUN
ejpam-6138	1	114	bayadh	bayadh	NOUN
ejpam-6138	1	115	,	,	PUNCT
ejpam-6138	1	116	32000	32000	NUM
ejpam-6138	1	117	,	,	PUNCT
ejpam-6138	1	118	algeria	algeria	PROPN
ejpam-6138	1	119	3	3	NUM
ejpam-6138	1	120	department	department	NOUN
ejpam-6138	1	121	of	of	ADP
ejpam-6138	1	122	mathematics	mathematic	NOUN
ejpam-6138	1	123	,	,	PUNCT
ejpam-6138	1	124	faculty	faculty	NOUN
ejpam-6138	1	125	of	of	ADP
ejpam-6138	1	126	science	science	NOUN
ejpam-6138	1	127	,	,	PUNCT
ejpam-6138	1	128	bu	bu	PROPN
ejpam-6138	1	129	-	-	PUNCT
ejpam-6138	1	130	ali	ali	PROPN
ejpam-6138	1	131	sina	sina	PROPN
ejpam-6138	1	132	university	university	PROPN
ejpam-6138	1	133	,	,	PUNCT
ejpam-6138	1	134	hamedan	hamedan	PROPN
ejpam-6138	1	135	,	,	PUNCT
ejpam-6138	1	136	iran	iran	PROPN
ejpam-6138	1	137	4	4	NUM
ejpam-6138	1	138	department	department	NOUN
ejpam-6138	1	139	of	of	ADP
ejpam-6138	1	140	mathematics	mathematic	NOUN
ejpam-6138	1	141	,	,	PUNCT
ejpam-6138	1	142	faculty	faculty	NOUN
ejpam-6138	1	143	of	of	ADP
ejpam-6138	1	144	arts	art	NOUN
ejpam-6138	1	145	and	and	CCONJ
ejpam-6138	1	146	sciences	science	NOUN
ejpam-6138	1	147	,	,	PUNCT
ejpam-6138	1	148	ondokuz	ondokuz	NOUN
ejpam-6138	1	149	mayis	mayis	PROPN
ejpam-6138	1	150	university	university	PROPN
ejpam-6138	1	151	,	,	PUNCT
ejpam-6138	1	152	55200	55200	NUM
ejpam-6138	1	153	atakum	atakum	NOUN
ejpam-6138	1	154	,	,	PUNCT
ejpam-6138	1	155	samsun	samsun	PROPN
ejpam-6138	1	156	,	,	PUNCT
ejpam-6138	1	157	turkey	turkey	PROPN
ejpam-6138	1	158	5	5	NUM
ejpam-6138	1	159	department	department	NOUN
ejpam-6138	1	160	of	of	ADP
ejpam-6138	1	161	mathematics	mathematic	NOUN
ejpam-6138	1	162	and	and	CCONJ
ejpam-6138	1	163	sciences	science	NOUN
ejpam-6138	1	164	,	,	PUNCT
ejpam-6138	1	165	prince	prince	PROPN
ejpam-6138	1	166	sultan	sultan	PROPN
ejpam-6138	1	167	university	university	PROPN
ejpam-6138	1	168	,	,	PUNCT
ejpam-6138	1	169	riyadh	riyadh	PROPN
ejpam-6138	1	170	11586	11586	NUM
ejpam-6138	1	171	,	,	PUNCT
ejpam-6138	1	172	saudi	saudi	PROPN
ejpam-6138	1	173	arabia	arabia	PROPN
ejpam-6138	1	174	abstract	abstract	NOUN
ejpam-6138	1	175	.	.	PUNCT
ejpam-6138	2	1	in	in	ADP
ejpam-6138	2	2	this	this	DET
ejpam-6138	2	3	paper	paper	NOUN
ejpam-6138	2	4	,	,	PUNCT
ejpam-6138	2	5	we	we	PRON
ejpam-6138	2	6	endeavor	endeavor	VERB
ejpam-6138	2	7	to	to	PART
ejpam-6138	2	8	simulate	simulate	VERB
ejpam-6138	2	9	the	the	DET
ejpam-6138	2	10	existence	existence	NOUN
ejpam-6138	2	11	of	of	ADP
ejpam-6138	2	12	a	a	DET
ejpam-6138	2	13	single	single	ADJ
ejpam-6138	2	14	solution	solution	NOUN
ejpam-6138	2	15	for	for	ADP
ejpam-6138	2	16	a	a	DET
ejpam-6138	2	17	bvp	bvp	NOUN
ejpam-6138	2	18	for	for	ADP
ejpam-6138	2	19	caputo	caputo	PROPN
ejpam-6138	2	20	-	-	PUNCT
ejpam-6138	2	21	katugampola	katugampola	PROPN
ejpam-6138	2	22	fractional	fractional	ADJ
ejpam-6138	2	23	derivative	derivative	NOUN
ejpam-6138	2	24	in	in	ADP
ejpam-6138	2	25	the	the	DET
ejpam-6138	2	26	manner	manner	NOUN
ejpam-6138	2	27	theorem	theorem	NOUN
ejpam-6138	2	28	of	of	ADP
ejpam-6138	2	29	contraction	contraction	NOUN
ejpam-6138	2	30	of	of	ADP
ejpam-6138	2	31	banach	banach	NOUN
ejpam-6138	2	32	.	.	PUNCT
ejpam-6138	3	1	we	we	PRON
ejpam-6138	3	2	extrapolate	extrapolate	VERB
ejpam-6138	3	3	similar	similar	ADJ
ejpam-6138	3	4	examples	example	NOUN
ejpam-6138	3	5	to	to	PART
ejpam-6138	3	6	interpret	interpret	VERB
ejpam-6138	3	7	the	the	DET
ejpam-6138	3	8	conclusions	conclusion	NOUN
ejpam-6138	3	9	reached	reach	VERB
ejpam-6138	3	10	.	.	PUNCT
ejpam-6138	4	1	2020	2020	NUM
ejpam-6138	4	2	mathematics	mathematics	PROPN
ejpam-6138	4	3	subject	subject	NOUN
ejpam-6138	4	4	classifications	classification	NOUN
ejpam-6138	4	5	:	:	PUNCT
ejpam-6138	4	6	26a33	26a33	NUM
ejpam-6138	4	7	,	,	PUNCT
ejpam-6138	4	8	65d05	65d05	NUM
ejpam-6138	4	9	,	,	PUNCT
ejpam-6138	4	10	65d30	65d30	ADJ
ejpam-6138	4	11	key	key	ADJ
ejpam-6138	4	12	words	word	NOUN
ejpam-6138	4	13	and	and	CCONJ
ejpam-6138	4	14	phrases	phrase	NOUN
ejpam-6138	4	15	:	:	PUNCT
ejpam-6138	4	16	banach	banach	NOUN
ejpam-6138	4	17	contraction	contraction	NOUN
ejpam-6138	4	18	theorem	theorem	VERB
ejpam-6138	4	19	,	,	PUNCT
ejpam-6138	4	20	caputo	caputo	PROPN
ejpam-6138	4	21	-	-	PUNCT
ejpam-6138	4	22	katugampola	katugampola	PROPN
ejpam-6138	4	23	fractional	fractional	PROPN
ejpam-6138	4	24	derivative	derivative	NOUN
ejpam-6138	4	25	,	,	PUNCT
ejpam-6138	4	26	bvp	bvp	NOUN
ejpam-6138	4	27	,	,	PUNCT
ejpam-6138	4	28	uniqueness	uniqueness	NOUN
ejpam-6138	4	29	and	and	CCONJ
ejpam-6138	4	30	existence	existence	NOUN
ejpam-6138	4	31	1	1	NUM
ejpam-6138	4	32	.	.	PUNCT
ejpam-6138	5	1	introduction	introduction	NOUN
ejpam-6138	5	2	fractional	fractional	ADJ
ejpam-6138	5	3	differential	differential	NOUN
ejpam-6138	5	4	equations	equation	NOUN
ejpam-6138	5	5	are	be	AUX
ejpam-6138	5	6	currently	currently	ADV
ejpam-6138	5	7	witnessing	witness	VERB
ejpam-6138	5	8	rapid	rapid	ADJ
ejpam-6138	5	9	development	development	NOUN
ejpam-6138	5	10	and	and	CCONJ
ejpam-6138	5	11	an	an	DET
ejpam-6138	5	12	advanced	advanced	ADJ
ejpam-6138	5	13	pace	pace	NOUN
ejpam-6138	5	14	of	of	ADP
ejpam-6138	5	15	research	research	NOUN
ejpam-6138	5	16	creativity	creativity	NOUN
ejpam-6138	5	17	.	.	PUNCT
ejpam-6138	6	1	this	this	PRON
ejpam-6138	6	2	is	be	AUX
ejpam-6138	6	3	due	due	ADJ
ejpam-6138	6	4	to	to	ADP
ejpam-6138	6	5	the	the	DET
ejpam-6138	6	6	growth	growth	NOUN
ejpam-6138	6	7	of	of	ADP
ejpam-6138	6	8	physical	physical	ADJ
ejpam-6138	6	9	,	,	PUNCT
ejpam-6138	6	10	technological	technological	ADJ
ejpam-6138	6	11	,	,	PUNCT
ejpam-6138	6	12	biological	biological	ADJ
ejpam-6138	6	13	,	,	PUNCT
ejpam-6138	6	14	economic	economic	ADJ
ejpam-6138	6	15	and	and	CCONJ
ejpam-6138	6	16	various	various	ADJ
ejpam-6138	6	17	new	new	ADJ
ejpam-6138	6	18	scientific	scientific	ADJ
ejpam-6138	6	19	phenomena	phenomenon	NOUN
ejpam-6138	6	20	.	.	PUNCT
ejpam-6138	7	1	mathematical	mathematical	ADJ
ejpam-6138	7	2	modeling	modeling	NOUN
ejpam-6138	7	3	plays	play	VERB
ejpam-6138	7	4	an	an	DET
ejpam-6138	7	5	important	important	ADJ
ejpam-6138	7	6	role	role	NOUN
ejpam-6138	7	7	in	in	ADP
ejpam-6138	7	8	the	the	DET
ejpam-6138	7	9	mathematical	mathematical	ADJ
ejpam-6138	7	10	interpretation	interpretation	NOUN
ejpam-6138	7	11	of	of	ADP
ejpam-6138	7	12	these	these	DET
ejpam-6138	7	13	various	various	ADJ
ejpam-6138	7	14	scientific	scientific	ADJ
ejpam-6138	7	15	phenomena	phenomenon	NOUN
ejpam-6138	7	16	.	.	PUNCT
ejpam-6138	8	1	it	it	PRON
ejpam-6138	8	2	produced	produce	VERB
ejpam-6138	8	3	ordinary	ordinary	ADJ
ejpam-6138	8	4	and	and	CCONJ
ejpam-6138	8	5	fractional	fractional	ADJ
ejpam-6138	8	6	differential	differential	ADJ
ejpam-6138	8	7	equations	equation	NOUN
ejpam-6138	8	8	,	,	PUNCT
ejpam-6138	8	9	as	as	ADV
ejpam-6138	8	10	well	well	ADV
ejpam-6138	8	11	as	as	ADP
ejpam-6138	8	12	partial	partial	ADJ
ejpam-6138	8	13	differential	differential	NOUN
ejpam-6138	8	14	equations	equation	NOUN
ejpam-6138	8	15	.	.	PUNCT
ejpam-6138	9	1	simulation	simulation	NOUN
ejpam-6138	9	2	is	be	AUX
ejpam-6138	9	3	also	also	ADV
ejpam-6138	9	4	of	of	ADP
ejpam-6138	9	5	great	great	ADJ
ejpam-6138	9	6	importance	importance	NOUN
ejpam-6138	9	7	in	in	ADP
ejpam-6138	9	8	providing	provide	VERB
ejpam-6138	9	9	analysis	analysis	NOUN
ejpam-6138	9	10	,	,	PUNCT
ejpam-6138	9	11	differentiated	differentiated	ADJ
ejpam-6138	9	12	deduction	deduction	NOUN
ejpam-6138	9	13	,	,	PUNCT
ejpam-6138	9	14	and	and	CCONJ
ejpam-6138	9	15	numerical	numerical	ADJ
ejpam-6138	9	16	interpretation	interpretation	NOUN
ejpam-6138	9	17	of	of	ADP
ejpam-6138	9	18	these	these	DET
ejpam-6138	9	19	recent	recent	ADJ
ejpam-6138	9	20	scientific	scientific	ADJ
ejpam-6138	9	21	phenomena	phenomenon	NOUN
ejpam-6138	9	22	,	,	PUNCT
ejpam-6138	9	23	the	the	DET
ejpam-6138	9	24	simulation	simulation	NOUN
ejpam-6138	9	25	∗	∗	VERB
ejpam-6138	9	26	corresponding	correspond	VERB
ejpam-6138	9	27	author	author	NOUN
ejpam-6138	9	28	.	.	PUNCT
ejpam-6138	10	1	doi	doi	NOUN
ejpam-6138	10	2	:	:	PUNCT
ejpam-6138	10	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6138	https://doi.org/10.29020/nybg.ejpam.v18i2.6138	NUM
ejpam-6138	10	4	email	email	NOUN
ejpam-6138	10	5	addresses	address	NOUN
ejpam-6138	10	6	:	:	PUNCT
ejpam-6138	10	7	zouaouizargui22@gmail.com	zouaouizargui22@gmail.com	X
ejpam-6138	10	8	(	(	PUNCT
ejpam-6138	10	9	z.	z.	PROPN
ejpam-6138	10	10	bekri	bekri	PROPN
ejpam-6138	10	11	)	)	PUNCT
ejpam-6138	10	12	,	,	PUNCT
ejpam-6138	10	13	mesamei@basu.ac.ir	mesamei@basu.ac.ir	PROPN
ejpam-6138	10	14	;	;	PUNCT
ejpam-6138	10	15	mesamei@gmail.com	mesamei@gmail.com	PROPN
ejpam-6138	10	16	(	(	PUNCT
ejpam-6138	10	17	m.	m.	PROPN
ejpam-6138	10	18	e.	e.	PROPN
ejpam-6138	10	19	samei	samei	PROPN
ejpam-6138	10	20	)	)	PUNCT
ejpam-6138	10	21	,	,	PUNCT
ejpam-6138	10	22	vserturk@omu.edu.tr	vserturk@omu.edu.tr	PROPN
ejpam-6138	10	23	(	(	PUNCT
ejpam-6138	10	24	v.	v.	ADP
ejpam-6138	10	25	s.	s.	PROPN
ejpam-6138	10	26	erturk	erturk	PROPN
ejpam-6138	10	27	)	)	PUNCT
ejpam-6138	10	28	,	,	PUNCT
ejpam-6138	10	29	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-6138	10	30	(	(	PUNCT
ejpam-6138	10	31	n.	n.	PROPN
ejpam-6138	10	32	mlaiki	mlaiki	PROPN
ejpam-6138	10	33	)	)	PUNCT
ejpam-6138	10	34	,	,	PUNCT
ejpam-6138	10	35	shaque@psu.edu.sa	shaque@psu.edu.sa	NOUN
ejpam-6138	10	36	(	(	PUNCT
ejpam-6138	10	37	s.	s.	PROPN
ejpam-6138	10	38	haque	haque	PROPN
ejpam-6138	10	39	)	)	PUNCT
ejpam-6138	10	40	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6138	10	41	1	1	NUM
ejpam-6138	10	42	copyright	copyright	NOUN
ejpam-6138	10	43	:	:	PUNCT
ejpam-6138	11	1	©	©	PROPN
ejpam-6138	11	2	2025	2025	NUM
ejpam-6138	11	3	the	the	DET
ejpam-6138	11	4	author(s	author(s	NOUN
ejpam-6138	11	5	)	)	PUNCT
ejpam-6138	11	6	.	.	PUNCT
ejpam-6138	12	1	(	(	PUNCT
ejpam-6138	12	2	cc	cc	NOUN
ejpam-6138	12	3	by	by	ADP
ejpam-6138	12	4	-	-	PUNCT
ejpam-6138	12	5	nc	nc	PROPN
ejpam-6138	12	6	4.0	4.0	NUM
ejpam-6138	12	7	)	)	PUNCT
ejpam-6138	12	8	z.	z.	PROPN
ejpam-6138	12	9	bekri	bekri	PROPN
ejpam-6138	12	10	et	et	PROPN
ejpam-6138	13	1	al	al	PROPN
ejpam-6138	13	2	.	.	PUNCT
ejpam-6138	13	3	/	/	SYM
ejpam-6138	13	4	eur	eur	PROPN
ejpam-6138	13	5	.	.	PUNCT
ejpam-6138	14	1	j.	j.	PROPN
ejpam-6138	14	2	pure	pure	PROPN
ejpam-6138	14	3	appl	appl	PROPN
ejpam-6138	14	4	.	.	PROPN
ejpam-6138	14	5	math	math	PROPN
ejpam-6138	14	6	,	,	PUNCT
ejpam-6138	14	7	18	18	NUM
ejpam-6138	14	8	(	(	PUNCT
ejpam-6138	14	9	2	2	NUM
ejpam-6138	14	10	)	)	PUNCT
ejpam-6138	14	11	(	(	PUNCT
ejpam-6138	14	12	2025	2025	NUM
ejpam-6138	14	13	)	)	PUNCT
ejpam-6138	14	14	,	,	PUNCT
ejpam-6138	14	15	6138	6138	NUM
ejpam-6138	14	16	2	2	NUM
ejpam-6138	14	17	of	of	ADP
ejpam-6138	14	18	17	17	NUM
ejpam-6138	14	19	used	use	VERB
ejpam-6138	14	20	in	in	ADP
ejpam-6138	14	21	this	this	DET
ejpam-6138	14	22	document	document	NOUN
ejpam-6138	14	23	is	be	AUX
ejpam-6138	14	24	a	a	DET
ejpam-6138	14	25	theoretical	theoretical	ADJ
ejpam-6138	14	26	simulation	simulation	NOUN
ejpam-6138	14	27	applied	apply	VERB
ejpam-6138	14	28	with	with	ADP
ejpam-6138	14	29	an	an	DET
ejpam-6138	14	30	ordinary	ordinary	ADJ
ejpam-6138	14	31	differential	differential	ADJ
ejpam-6138	14	32	equation	equation	NOUN
ejpam-6138	14	33	to	to	ADP
ejpam-6138	14	34	a	a	DET
ejpam-6138	14	35	fractional	fractional	ADJ
ejpam-6138	14	36	differential	differential	ADJ
ejpam-6138	14	37	equation	equation	NOUN
ejpam-6138	14	38	[	[	X
ejpam-6138	14	39	1–12	1–12	NOUN
ejpam-6138	14	40	]	]	PUNCT
ejpam-6138	14	41	.	.	PUNCT
ejpam-6138	15	1	the	the	DET
ejpam-6138	15	2	following	follow	VERB
ejpam-6138	15	3	simulation	simulation	NOUN
ejpam-6138	15	4	is	be	AUX
ejpam-6138	15	5	derived	derive	VERB
ejpam-6138	15	6	from	from	ADP
ejpam-6138	15	7	one	one	NUM
ejpam-6138	15	8	of	of	ADP
ejpam-6138	15	9	the	the	DET
ejpam-6138	15	10	theorems	theorem	NOUN
ejpam-6138	15	11	declared	declare	VERB
ejpam-6138	15	12	in	in	ADP
ejpam-6138	15	13	[	[	PUNCT
ejpam-6138	15	14	13	13	NUM
ejpam-6138	15	15	]	]	PUNCT
ejpam-6138	15	16	,	,	PUNCT
ejpam-6138	15	17	which	which	PRON
ejpam-6138	15	18	was	be	AUX
ejpam-6138	15	19	also	also	ADV
ejpam-6138	15	20	classified	classify	VERB
ejpam-6138	15	21	without	without	ADP
ejpam-6138	15	22	proof	proof	NOUN
ejpam-6138	15	23	in	in	ADP
ejpam-6138	15	24	[	[	X
ejpam-6138	15	25	14	14	NUM
ejpam-6138	15	26	,	,	PUNCT
ejpam-6138	15	27	theorem	theorem	VERB
ejpam-6138	15	28	3.3	3.3	NUM
ejpam-6138	15	29	]	]	PUNCT
ejpam-6138	15	30	and	and	CCONJ
ejpam-6138	15	31	it	it	PRON
ejpam-6138	15	32	remained	remain	VERB
ejpam-6138	15	33	as	as	ADP
ejpam-6138	15	34	a	a	DET
ejpam-6138	15	35	neglected	neglect	VERB
ejpam-6138	15	36	issue	issue	NOUN
ejpam-6138	15	37	without	without	ADP
ejpam-6138	15	38	a	a	DET
ejpam-6138	15	39	solution	solution	NOUN
ejpam-6138	15	40	[	[	X
ejpam-6138	15	41	15	15	NUM
ejpam-6138	15	42	,	,	PUNCT
ejpam-6138	15	43	problem	problem	NOUN
ejpam-6138	15	44	(	(	PUNCT
ejpam-6138	15	45	41.6	41.6	NUM
ejpam-6138	15	46	)	)	PUNCT
ejpam-6138	15	47	]	]	PUNCT
ejpam-6138	15	48	for	for	ADP
ejpam-6138	15	49	the	the	DET
ejpam-6138	15	50	researcher	researcher	NOUN
ejpam-6138	15	51	.	.	PUNCT
ejpam-6138	16	1	theorem	theorem	NOUN
ejpam-6138	16	2	1	1	NUM
ejpam-6138	16	3	(	(	PUNCT
ejpam-6138	16	4	[	[	X
ejpam-6138	16	5	13	13	NUM
ejpam-6138	16	6	]	]	NUM
ejpam-6138	16	7	)	)	PUNCT
ejpam-6138	16	8	.	.	PUNCT
ejpam-6138	17	1	presume	presume	VERB
ejpam-6138	17	2	ξ	ξ	PROPN
ejpam-6138	17	3	∶	∶	NOUN
ejpam-6138	17	4	[	[	X
ejpam-6138	17	5	θ	θ	NOUN
ejpam-6138	17	6	,	,	PUNCT
ejpam-6138	17	7	ϑ]×r2	ϑ]×r2	NOUN
ejpam-6138	17	8	⟶	⟶	NOUN
ejpam-6138	17	9	r	r	NOUN
ejpam-6138	17	10	is	be	AUX
ejpam-6138	17	11	a	a	DET
ejpam-6138	17	12	function	function	NOUN
ejpam-6138	17	13	is	be	AUX
ejpam-6138	17	14	continuous	continuous	ADJ
ejpam-6138	17	15	and	and	CCONJ
ejpam-6138	17	16	verifies	verifie	NOUN
ejpam-6138	17	17	a	a	DET
ejpam-6138	17	18	condition	condition	NOUN
ejpam-6138	17	19	of	of	ADP
ejpam-6138	17	20	uniform	uniform	ADJ
ejpam-6138	17	21	lipschitz	lipschitz	NOUN
ejpam-6138	17	22	with	with	ADP
ejpam-6138	17	23	reference	reference	NOUN
ejpam-6138	17	24	to	to	ADP
ejpam-6138	17	25	µ	µ	PROPN
ejpam-6138	17	26	and	and	CCONJ
ejpam-6138	17	27	µ	µ	NOUN
ejpam-6138	17	28	′	′	NUM
ejpam-6138	17	29	»	»	PUNCT
ejpam-6138	17	30	»	»	PUNCT
ejpam-6138	17	31	»	»	PRON
ejpam-6138	17	32	»	»	PUNCT
ejpam-6138	17	33	»	»	PUNCT
ejpam-6138	17	34	»	»	X
ejpam-6138	17	35	ξ	ξ	X
ejpam-6138	17	36	(	(	PUNCT
ejpam-6138	17	37	τ	τ	PROPN
ejpam-6138	17	38	,	,	PUNCT
ejpam-6138	17	39	µ	µ	NOUN
ejpam-6138	17	40	,	,	PUNCT
ejpam-6138	17	41	µ′	µ′	NUM
ejpam-6138	17	42	)	)	PUNCT
ejpam-6138	18	1	−	−	PROPN
ejpam-6138	18	2	ξ	ξ	X
ejpam-6138	18	3	(	(	PUNCT
ejpam-6138	18	4	τ	τ	PROPN
ejpam-6138	18	5	,	,	PUNCT
ejpam-6138	18	6	ν	ν	PROPN
ejpam-6138	18	7	,	,	PUNCT
ejpam-6138	18	8	ν	ν	NOUN
ejpam-6138	18	9	′	′	NOUN
ejpam-6138	18	10	)	)	PUNCT
ejpam-6138	18	11	»	»	PRON
ejpam-6138	18	12	»	»	PUNCT
ejpam-6138	18	13	»	»	PUNCT
ejpam-6138	18	14	»	»	PRON
ejpam-6138	18	15	»	»	ADV
ejpam-6138	18	16	»	»	X
ejpam-6138	18	17	≤	≤	X
ejpam-6138	18	18	ζ∣µ	ζ∣µ	PUNCT
ejpam-6138	18	19	−	−	PROPN
ejpam-6138	18	20	ν∣	ν∣	NOUN
ejpam-6138	18	21	+	+	PUNCT
ejpam-6138	18	22	η∣µ′	η∣µ′	NOUN
ejpam-6138	18	23	−	−	NOUN
ejpam-6138	18	24	ν	ν	NOUN
ejpam-6138	18	25	′∣	′∣	PROPN
ejpam-6138	18	26	,	,	PUNCT
ejpam-6138	18	27	(	(	PUNCT
ejpam-6138	18	28	1.1	1.1	NUM
ejpam-6138	18	29	)	)	PUNCT
ejpam-6138	18	30	for	for	ADP
ejpam-6138	18	31	(	(	PUNCT
ejpam-6138	18	32	τ	τ	PROPN
ejpam-6138	18	33	,	,	PUNCT
ejpam-6138	18	34	µ	µ	NOUN
ejpam-6138	18	35	,	,	PUNCT
ejpam-6138	18	36	µ′	µ′	NOUN
ejpam-6138	18	37	)	)	PUNCT
ejpam-6138	18	38	,	,	PUNCT
ejpam-6138	18	39	(	(	PUNCT
ejpam-6138	18	40	τ	τ	X
ejpam-6138	18	41	,	,	PUNCT
ejpam-6138	18	42	ν	ν	PROPN
ejpam-6138	18	43	,	,	PUNCT
ejpam-6138	18	44	ν	ν	NOUN
ejpam-6138	18	45	′	′	NOUN
ejpam-6138	18	46	)	)	PUNCT
ejpam-6138	18	47	∈	∈	PROPN
ejpam-6138	19	1	[	[	X
ejpam-6138	19	2	θ	θ	X
ejpam-6138	19	3	,	,	PUNCT
ejpam-6138	19	4	ϑ	ϑ	X
ejpam-6138	19	5	]	]	X
ejpam-6138	19	6	×	×	NOUN
ejpam-6138	19	7	r2	r2	NOUN
ejpam-6138	19	8	,	,	PUNCT
ejpam-6138	19	9	where	where	SCONJ
ejpam-6138	19	10	ζ	ζ	NOUN
ejpam-6138	19	11	≥	≥	NOUN
ejpam-6138	19	12	0	0	NUM
ejpam-6138	19	13	and	and	CCONJ
ejpam-6138	19	14	η	η	PROPN
ejpam-6138	19	15	>	>	X
ejpam-6138	19	16	0	0	NUM
ejpam-6138	19	17	are	be	AUX
ejpam-6138	19	18	reals	real	NOUN
ejpam-6138	19	19	.	.	PUNCT
ejpam-6138	20	1	if	if	SCONJ
ejpam-6138	20	2	ζ	ζ	X
ejpam-6138	20	3	(	(	PUNCT
ejpam-6138	20	4	ϑ−θ)2	ϑ−θ)2	NOUN
ejpam-6138	20	5	8	8	NUM
ejpam-6138	20	6	+	+	CCONJ
ejpam-6138	20	7	η	η	PROPN
ejpam-6138	20	8	(	(	PUNCT
ejpam-6138	20	9	ϑ−θ	ϑ−θ	NOUN
ejpam-6138	20	10	)	)	PUNCT
ejpam-6138	20	11	2	2	NUM
ejpam-6138	20	12	<	<	X
ejpam-6138	20	13	1	1	NUM
ejpam-6138	20	14	,	,	PUNCT
ejpam-6138	20	15	(	(	PUNCT
ejpam-6138	20	16	1.2	1.2	NUM
ejpam-6138	20	17	)	)	PUNCT
ejpam-6138	20	18	so	so	SCONJ
ejpam-6138	20	19	the	the	DET
ejpam-6138	20	20	bvp	bvp	PROPN
ejpam-6138	20	21	µ	µ	PRON
ejpam-6138	20	22	′′	′′	PROPN
ejpam-6138	20	23	=	=	SYM
ejpam-6138	20	24	−ξ	−ξ	NOUN
ejpam-6138	20	25	(	(	PUNCT
ejpam-6138	20	26	τ	τ	PROPN
ejpam-6138	20	27	,	,	PUNCT
ejpam-6138	20	28	µ	µ	NOUN
ejpam-6138	20	29	,	,	PUNCT
ejpam-6138	20	30	µ′	µ′	NUM
ejpam-6138	20	31	)	)	PUNCT
ejpam-6138	20	32	,	,	PUNCT
ejpam-6138	20	33	µ(θ	µ(θ	PROPN
ejpam-6138	20	34	)	)	PUNCT
ejpam-6138	20	35	=	=	SYM
ejpam-6138	20	36	λ1	λ1	ADJ
ejpam-6138	20	37	,	,	PUNCT
ejpam-6138	20	38	µ(ϑ	µ(ϑ	PROPN
ejpam-6138	20	39	)	)	PUNCT
ejpam-6138	20	40	=	=	SYM
ejpam-6138	20	41	λ2	λ2	NOUN
ejpam-6138	20	42	,	,	PUNCT
ejpam-6138	20	43	(	(	PUNCT
ejpam-6138	20	44	1.3	1.3	NUM
ejpam-6138	20	45	)	)	PUNCT
ejpam-6138	20	46	admits	admit	VERB
ejpam-6138	20	47	a	a	DET
ejpam-6138	20	48	unique	unique	ADJ
ejpam-6138	20	49	solution	solution	NOUN
ejpam-6138	20	50	.	.	PUNCT
ejpam-6138	21	1	in	in	ADP
ejpam-6138	21	2	the	the	DET
ejpam-6138	21	3	content	content	NOUN
ejpam-6138	21	4	of	of	ADP
ejpam-6138	21	5	this	this	DET
ejpam-6138	21	6	article	article	NOUN
ejpam-6138	21	7	,	,	PUNCT
ejpam-6138	21	8	we	we	PRON
ejpam-6138	21	9	intend	intend	VERB
ejpam-6138	21	10	to	to	PART
ejpam-6138	21	11	develop	develop	VERB
ejpam-6138	21	12	the	the	DET
ejpam-6138	21	13	aforementioned	aforementioned	ADJ
ejpam-6138	21	14	consequences	consequence	NOUN
ejpam-6138	21	15	through	through	ADP
ejpam-6138	21	16	viewing	view	VERB
ejpam-6138	21	17	of	of	ADP
ejpam-6138	21	18	a	a	DET
ejpam-6138	21	19	fractional	fractional	ADJ
ejpam-6138	21	20	generalized	generalize	VERB
ejpam-6138	21	21	caputo	caputo	PROPN
ejpam-6138	21	22	derivative	derivative	NOUN
ejpam-6138	21	23	(	(	PUNCT
ejpam-6138	21	24	we	we	PRON
ejpam-6138	21	25	advise	advise	VERB
ejpam-6138	21	26	the	the	DET
ejpam-6138	21	27	researcher	researcher	NOUN
ejpam-6138	21	28	to	to	PART
ejpam-6138	21	29	see	see	VERB
ejpam-6138	21	30	[	[	X
ejpam-6138	21	31	16–23	16–23	NUM
ejpam-6138	21	32	]	]	PUNCT
ejpam-6138	21	33	in	in	ADP
ejpam-6138	21	34	order	order	NOUN
ejpam-6138	21	35	to	to	ADP
ejpam-6138	21	36	the	the	DET
ejpam-6138	21	37	fundamental	fundamental	ADJ
ejpam-6138	21	38	concepts	concept	NOUN
ejpam-6138	21	39	and	and	CCONJ
ejpam-6138	21	40	basic	basic	ADJ
ejpam-6138	21	41	consequences	consequence	NOUN
ejpam-6138	21	42	on	on	ADP
ejpam-6138	21	43	calculus	calculus	NOUN
ejpam-6138	21	44	of	of	ADP
ejpam-6138	21	45	fractional	fractional	ADJ
ejpam-6138	21	46	order	order	NOUN
ejpam-6138	21	47	with	with	ADP
ejpam-6138	21	48	applications	application	NOUN
ejpam-6138	21	49	)	)	PUNCT
ejpam-6138	21	50	instead	instead	ADV
ejpam-6138	21	51	of	of	ADP
ejpam-6138	21	52	the	the	DET
ejpam-6138	21	53	ordinary	ordinary	ADJ
ejpam-6138	21	54	operator	operator	NOUN
ejpam-6138	21	55	µ	µ	PRON
ejpam-6138	21	56	′′	′′	PROPN
ejpam-6138	21	57	,	,	PUNCT
ejpam-6138	21	58	that	that	PRON
ejpam-6138	21	59	is	be	AUX
ejpam-6138	21	60	to	to	PART
ejpam-6138	21	61	say	say	VERB
ejpam-6138	21	62	,	,	PUNCT
ejpam-6138	21	63	we	we	PRON
ejpam-6138	21	64	achieve	achieve	VERB
ejpam-6138	21	65	the	the	DET
ejpam-6138	21	66	existence	existence	NOUN
ejpam-6138	21	67	of	of	ADP
ejpam-6138	21	68	a	a	DET
ejpam-6138	21	69	singularity	singularity	NOUN
ejpam-6138	21	70	of	of	ADP
ejpam-6138	21	71	solution	solution	NOUN
ejpam-6138	21	72	to	to	ADP
ejpam-6138	21	73	the	the	DET
ejpam-6138	21	74	bvp	bvp	NOUN
ejpam-6138	21	75	of	of	ADP
ejpam-6138	21	76	caputo	caputo	PROPN
ejpam-6138	21	77	-	-	PUNCT
ejpam-6138	21	78	katugampola	katugampola	PROPN
ejpam-6138	21	79	fractional	fractional	ADJ
ejpam-6138	21	80	derivative	derivative	ADJ
ejpam-6138	21	81	order	order	NOUN
ejpam-6138	21	82	{	{	PUNCT
ejpam-6138	21	83	ϱ	ϱ	PROPN
ejpam-6138	21	84	cd	cd	PROPN
ejpam-6138	21	85	σ	σ	PROPN
ejpam-6138	21	86	θ+µ(τ	θ+µ(τ	PROPN
ejpam-6138	21	87	)	)	PUNCT
ejpam-6138	22	1	=	=	SYM
ejpam-6138	22	2	−ξ	−ξ	NOUN
ejpam-6138	22	3	(	(	PUNCT
ejpam-6138	22	4	τ	τ	PROPN
ejpam-6138	22	5	,	,	PUNCT
ejpam-6138	22	6	µ(τ	µ(τ	PROPN
ejpam-6138	22	7	)	)	PUNCT
ejpam-6138	22	8	,	,	PUNCT
ejpam-6138	22	9	ϱcdς	ϱcdς	ADJ
ejpam-6138	22	10	θ+µ(τ	θ+µ(τ	NOUN
ejpam-6138	22	11	)	)	PUNCT
ejpam-6138	22	12	)	)	PUNCT
ejpam-6138	22	13	,	,	PUNCT
ejpam-6138	23	1	θ	θ	X
ejpam-6138	23	2	<	<	X
ejpam-6138	23	3	τ	τ	X
ejpam-6138	23	4	<	<	X
ejpam-6138	23	5	ϑ	ϑ	X
ejpam-6138	23	6	,	,	PUNCT
ejpam-6138	23	7	µ(θ	µ(θ	ADJ
ejpam-6138	23	8	)	)	PUNCT
ejpam-6138	23	9	=	=	SYM
ejpam-6138	23	10	λ1	λ1	ADJ
ejpam-6138	23	11	,	,	PUNCT
ejpam-6138	23	12	µ(ϑ	µ(ϑ	PROPN
ejpam-6138	23	13	)	)	PUNCT
ejpam-6138	23	14	=	=	SYM
ejpam-6138	23	15	λ2	λ2	NOUN
ejpam-6138	23	16	,	,	PUNCT
ejpam-6138	23	17	(	(	PUNCT
ejpam-6138	23	18	1.4	1.4	NUM
ejpam-6138	23	19	)	)	PUNCT
ejpam-6138	23	20	where	where	SCONJ
ejpam-6138	23	21	1	1	NUM
ejpam-6138	23	22	<	<	X
ejpam-6138	23	23	σ	σ	X
ejpam-6138	23	24	≤	≤	NUM
ejpam-6138	23	25	2	2	NUM
ejpam-6138	23	26	,	,	PUNCT
ejpam-6138	23	27	0	0	PUNCT
ejpam-6138	23	28	<	<	X
ejpam-6138	23	29	ς	ς	PROPN
ejpam-6138	23	30	≤	≤	ADV
ejpam-6138	23	31	1	1	NUM
ejpam-6138	23	32	.	.	PUNCT
ejpam-6138	24	1	previously	previously	ADV
ejpam-6138	24	2	,	,	PUNCT
ejpam-6138	24	3	we	we	PRON
ejpam-6138	24	4	searched	search	VERB
ejpam-6138	24	5	the	the	DET
ejpam-6138	24	6	existence	existence	NOUN
ejpam-6138	24	7	of	of	ADP
ejpam-6138	24	8	a	a	DET
ejpam-6138	24	9	singularity	singularity	NOUN
ejpam-6138	24	10	of	of	ADP
ejpam-6138	24	11	a	a	DET
ejpam-6138	24	12	solve	solve	NOUN
ejpam-6138	24	13	to	to	ADP
ejpam-6138	24	14	the	the	DET
ejpam-6138	24	15	boundary	boundary	ADJ
ejpam-6138	24	16	value	value	NOUN
ejpam-6138	24	17	problem	problem	NOUN
ejpam-6138	24	18	for	for	ADP
ejpam-6138	24	19	caputo	caputo	PROPN
ejpam-6138	24	20	-	-	PUNCT
ejpam-6138	24	21	katugampola	katugampola	PROPN
ejpam-6138	24	22	fractional	fractional	ADJ
ejpam-6138	24	23	derivative	derivative	NOUN
ejpam-6138	24	24	(	(	PUNCT
ejpam-6138	24	25	see	see	VERB
ejpam-6138	24	26	,	,	PUNCT
ejpam-6138	24	27	[	[	X
ejpam-6138	24	28	24	24	NUM
ejpam-6138	24	29	]	]	PUNCT
ejpam-6138	24	30	)	)	PUNCT
ejpam-6138	24	31	and	and	CCONJ
ejpam-6138	24	32	the	the	DET
ejpam-6138	24	33	references	reference	NOUN
ejpam-6138	24	34	mentioned	mention	VERB
ejpam-6138	24	35	in	in	ADP
ejpam-6138	24	36	its	its	PRON
ejpam-6138	24	37	content	content	NOUN
ejpam-6138	24	38	)	)	PUNCT
ejpam-6138	24	39	.	.	PUNCT
ejpam-6138	25	1	under	under	ADP
ejpam-6138	25	2	previous	previous	ADJ
ejpam-6138	25	3	research	research	NOUN
ejpam-6138	25	4	,	,	PUNCT
ejpam-6138	25	5	the	the	DET
ejpam-6138	25	6	simulation	simulation	NOUN
ejpam-6138	25	7	of	of	ADP
ejpam-6138	25	8	our	our	PRON
ejpam-6138	25	9	problem	problem	NOUN
ejpam-6138	25	10	produces	produce	VERB
ejpam-6138	25	11	new	new	ADJ
ejpam-6138	25	12	results	result	NOUN
ejpam-6138	25	13	by	by	ADP
ejpam-6138	25	14	applying	apply	VERB
ejpam-6138	25	15	theorem	theorem	NOUN
ejpam-6138	25	16	1	1	NUM
ejpam-6138	25	17	.	.	NOUN
ejpam-6138	25	18	2	2	NUM
ejpam-6138	25	19	.	.	PUNCT
ejpam-6138	25	20	principal	principal	ADJ
ejpam-6138	25	21	concepts	concept	NOUN
ejpam-6138	25	22	starting	start	VERB
ejpam-6138	25	23	,	,	PUNCT
ejpam-6138	25	24	we	we	PRON
ejpam-6138	25	25	review	review	VERB
ejpam-6138	25	26	some	some	DET
ejpam-6138	25	27	basic	basic	ADJ
ejpam-6138	25	28	properties	property	NOUN
ejpam-6138	25	29	of	of	ADP
ejpam-6138	25	30	fractional	fractional	ADJ
ejpam-6138	25	31	calculus	calculus	NOUN
ejpam-6138	25	32	for	for	ADP
ejpam-6138	25	33	investigating	investigate	VERB
ejpam-6138	25	34	bvps	bvps	NOUN
ejpam-6138	25	35	,	,	PUNCT
ejpam-6138	25	36	lookup	lookup	NOUN
ejpam-6138	25	37	in	in	ADP
ejpam-6138	25	38	[	[	X
ejpam-6138	25	39	25–29	25–29	NOUN
ejpam-6138	25	40	]	]	PUNCT
ejpam-6138	25	41	.	.	PUNCT
ejpam-6138	26	1	definition	definition	NOUN
ejpam-6138	26	2	1	1	NUM
ejpam-6138	26	3	.	.	PUNCT
ejpam-6138	27	1	on	on	ADP
ejpam-6138	27	2	the	the	DET
ejpam-6138	27	3	left	left	ADV
ejpam-6138	27	4	-	-	PUNCT
ejpam-6138	27	5	sided	sided	ADJ
ejpam-6138	27	6	in	in	ADP
ejpam-6138	27	7	the	the	DET
ejpam-6138	27	8	generalized	generalized	ADJ
ejpam-6138	27	9	fractional	fractional	ADJ
ejpam-6138	27	10	integral	integral	ADJ
ejpam-6138	27	11	order	order	NOUN
ejpam-6138	27	12	ϱ	ϱ	ADP
ejpam-6138	27	13	i	i	PROPN
ejpam-6138	27	14	σ	σ	PROPN
ejpam-6138	27	15	θ+µ	θ+µ	NUM
ejpam-6138	27	16	for	for	ADP
ejpam-6138	27	17	σ	σ	PROPN
ejpam-6138	27	18	∈	∈	PROPN
ejpam-6138	27	19	c(re(σ	c(re(σ	PROPN
ejpam-6138	27	20	)	)	PUNCT
ejpam-6138	27	21	>	>	X
ejpam-6138	27	22	0	0	NUM
ejpam-6138	27	23	)	)	PUNCT
ejpam-6138	27	24	is	be	AUX
ejpam-6138	27	25	given	give	VERB
ejpam-6138	27	26	by	by	ADP
ejpam-6138	27	27	(	(	PUNCT
ejpam-6138	27	28	ϱiσθ+µ	ϱiσθ+µ	INTJ
ejpam-6138	27	29	)	)	PUNCT
ejpam-6138	27	30	(	(	PUNCT
ejpam-6138	27	31	τ	τ	X
ejpam-6138	27	32	)	)	PUNCT
ejpam-6138	27	33	=	=	PUNCT
ejpam-6138	27	34	ϱ	ϱ	ADP
ejpam-6138	27	35	1−σ	1−σ	NUM
ejpam-6138	27	36	γ(σ	γ(σ	PROPN
ejpam-6138	27	37	)	)	PUNCT
ejpam-6138	27	38	∫	∫	PROPN
ejpam-6138	28	1	τ	τ	PROPN
ejpam-6138	28	2	θ	θ	PROPN
ejpam-6138	28	3	r	r	NOUN
ejpam-6138	28	4	ϱ−1(τϱ	ϱ−1(τϱ	PROPN
ejpam-6138	28	5	−	−	NOUN
ejpam-6138	28	6	r	r	NOUN
ejpam-6138	28	7	ϱ)σ−1µ(r)dr	ϱ)σ−1µ(r)dr	NOUN
ejpam-6138	28	8	,	,	PUNCT
ejpam-6138	28	9	(	(	PUNCT
ejpam-6138	28	10	2.1	2.1	NUM
ejpam-6138	28	11	)	)	PUNCT
ejpam-6138	28	12	z.	z.	PROPN
ejpam-6138	28	13	bekri	bekri	PROPN
ejpam-6138	28	14	et	et	PROPN
ejpam-6138	28	15	al	al	PROPN
ejpam-6138	28	16	.	.	PUNCT
ejpam-6138	28	17	/	/	SYM
ejpam-6138	28	18	eur	eur	PROPN
ejpam-6138	28	19	.	.	PUNCT
ejpam-6138	29	1	j.	j.	PROPN
ejpam-6138	29	2	pure	pure	PROPN
ejpam-6138	29	3	appl	appl	PROPN
ejpam-6138	29	4	.	.	PROPN
ejpam-6138	29	5	math	math	PROPN
ejpam-6138	29	6	,	,	PUNCT
ejpam-6138	29	7	18	18	NUM
ejpam-6138	29	8	(	(	PUNCT
ejpam-6138	29	9	2	2	NUM
ejpam-6138	29	10	)	)	PUNCT
ejpam-6138	29	11	(	(	PUNCT
ejpam-6138	29	12	2025	2025	NUM
ejpam-6138	29	13	)	)	PUNCT
ejpam-6138	29	14	,	,	PUNCT
ejpam-6138	29	15	6138	6138	NUM
ejpam-6138	29	16	3	3	NUM
ejpam-6138	29	17	of	of	ADP
ejpam-6138	29	18	17	17	NUM
ejpam-6138	29	19	where	where	SCONJ
ejpam-6138	29	20	τ	τ	PROPN
ejpam-6138	29	21	>	>	X
ejpam-6138	29	22	0	0	PROPN
ejpam-6138	29	23	,	,	PUNCT
ejpam-6138	29	24	ϱ	ϱ	ADP
ejpam-6138	29	25	>	>	X
ejpam-6138	29	26	0	0	NUM
ejpam-6138	29	27	.	.	PUNCT
ejpam-6138	30	1	according	accord	VERB
ejpam-6138	30	2	to	to	ADP
ejpam-6138	30	3	the	the	DET
ejpam-6138	30	4	formula	formula	NOUN
ejpam-6138	30	5	of	of	ADP
ejpam-6138	30	6	the	the	DET
ejpam-6138	30	7	generalized	generalize	VERB
ejpam-6138	30	8	fractional	fractional	ADJ
ejpam-6138	30	9	integrals	integral	NOUN
ejpam-6138	30	10	(	(	PUNCT
ejpam-6138	30	11	2.1	2.1	NUM
ejpam-6138	30	12	)	)	PUNCT
ejpam-6138	30	13	,	,	PUNCT
ejpam-6138	30	14	we	we	PRON
ejpam-6138	30	15	define	define	VERB
ejpam-6138	30	16	the	the	DET
ejpam-6138	30	17	caputo	caputo	PROPN
ejpam-6138	30	18	-	-	PUNCT
ejpam-6138	30	19	katugampola	katugampola	PROPN
ejpam-6138	30	20	fractional	fractional	ADJ
ejpam-6138	30	21	derivative	derivative	NOUN
ejpam-6138	30	22	for	for	ADP
ejpam-6138	30	23	τ	τ	PROPN
ejpam-6138	30	24	>	>	X
ejpam-6138	30	25	0	0	PUNCT
ejpam-6138	31	1	by	by	ADP
ejpam-6138	31	2	(	(	PUNCT
ejpam-6138	31	3	ϱdσ	ϱdσ	PROPN
ejpam-6138	31	4	θ+µ	θ+µ	NUM
ejpam-6138	31	5	)	)	PUNCT
ejpam-6138	31	6	(	(	PUNCT
ejpam-6138	31	7	τ	τ	X
ejpam-6138	31	8	)	)	PUNCT
ejpam-6138	31	9	=	=	SYM
ejpam-6138	31	10	(	(	PUNCT
ejpam-6138	31	11	τ1−ϱ	τ1−ϱ	PROPN
ejpam-6138	31	12	d	d	PROPN
ejpam-6138	31	13	dτ	dτ	NOUN
ejpam-6138	31	14	)	)	PUNCT
ejpam-6138	31	15	n	n	CCONJ
ejpam-6138	31	16	(	(	PUNCT
ejpam-6138	31	17	ϱin−σθ+	ϱin−σθ+	PROPN
ejpam-6138	31	18	µ	µ	NUM
ejpam-6138	31	19	)	)	PUNCT
ejpam-6138	31	20	(	(	PUNCT
ejpam-6138	31	21	τ	τ	X
ejpam-6138	31	22	)	)	PUNCT
ejpam-6138	31	23	=	=	PUNCT
ejpam-6138	31	24	ϱ	ϱ	ADP
ejpam-6138	31	25	σ−n+1	σ−n+1	PROPN
ejpam-6138	31	26	γ(n−σ	γ(n−σ	PROPN
ejpam-6138	31	27	)	)	PUNCT
ejpam-6138	31	28	(	(	PUNCT
ejpam-6138	31	29	τ	τ	PROPN
ejpam-6138	31	30	1−ϱ	1−ϱ	PROPN
ejpam-6138	31	31	d	d	PROPN
ejpam-6138	31	32	dτ	dτ	NOUN
ejpam-6138	31	33	)	)	PUNCT
ejpam-6138	31	34	n	n	CCONJ
ejpam-6138	31	35	∫	∫	NOUN
ejpam-6138	31	36	τ	τ	PROPN
ejpam-6138	31	37	θ	θ	PROPN
ejpam-6138	31	38	r	r	NOUN
ejpam-6138	31	39	ϱ−1(τϱ	ϱ−1(τϱ	PROPN
ejpam-6138	31	40	−	−	NOUN
ejpam-6138	31	41	r	r	NOUN
ejpam-6138	31	42	ϱ)n−1−σµ(r	ϱ)n−1−σµ(r	NOUN
ejpam-6138	31	43	)	)	PUNCT
ejpam-6138	31	44	dr	dr	PROPN
ejpam-6138	31	45	.	.	PROPN
ejpam-6138	31	46	(	(	PUNCT
ejpam-6138	31	47	2.2	2.2	NUM
ejpam-6138	31	48	)	)	PUNCT
ejpam-6138	31	49	definition	definition	NOUN
ejpam-6138	31	50	2	2	NUM
ejpam-6138	31	51	.	.	PUNCT
ejpam-6138	31	52	by	by	ADP
ejpam-6138	31	53	using	use	VERB
ejpam-6138	31	54	the	the	DET
ejpam-6138	31	55	above	above	ADJ
ejpam-6138	31	56	caputo	caputo	PROPN
ejpam-6138	31	57	-	-	PUNCT
ejpam-6138	31	58	katugampola	katugampola	PROPN
ejpam-6138	31	59	fractional	fractional	ADJ
ejpam-6138	31	60	derivative	derivative	NOUN
ejpam-6138	31	61	(	(	PUNCT
ejpam-6138	31	62	2.2	2.2	NUM
ejpam-6138	31	63	)	)	PUNCT
ejpam-6138	31	64	,	,	PUNCT
ejpam-6138	31	65	the	the	DET
ejpam-6138	31	66	generalized	generalize	VERB
ejpam-6138	31	67	caputo	caputo	PROPN
ejpam-6138	31	68	non	non	ADJ
ejpam-6138	31	69	-	-	ADJ
ejpam-6138	31	70	classical	classical	ADJ
ejpam-6138	31	71	derivative	derivative	NOUN
ejpam-6138	31	72	with	with	ADP
ejpam-6138	31	73	the	the	DET
ejpam-6138	31	74	operator	operator	NOUN
ejpam-6138	31	75	notation	notation	NOUN
ejpam-6138	31	76	ϱ	ϱ	PROPN
ejpam-6138	31	77	cd	cd	PROPN
ejpam-6138	31	78	σ	σ	PROPN
ejpam-6138	31	79	θ+	θ+	PROPN
ejpam-6138	31	80	is	be	AUX
ejpam-6138	31	81	displayed	display	VERB
ejpam-6138	31	82	by	by	ADP
ejpam-6138	31	83	ϱ	ϱ	PROPN
ejpam-6138	31	84	cd	cd	PROPN
ejpam-6138	31	85	σ	σ	PROPN
ejpam-6138	31	86	θ+µ(τ	θ+µ(τ	PROPN
ejpam-6138	31	87	)	)	PUNCT
ejpam-6138	31	88	=	=	NOUN
ejpam-6138	31	89	(	(	PUNCT
ejpam-6138	31	90	ϱ	ϱ	PROPN
ejpam-6138	31	91	d	d	PROPN
ejpam-6138	31	92	σ	σ	PROPN
ejpam-6138	31	93	θ+[µ(τ	θ+[µ(τ	PROPN
ejpam-6138	31	94	)	)	PUNCT
ejpam-6138	32	1	−	−	PROPN
ejpam-6138	32	2	n−1	n−1	PROPN
ejpam-6138	32	3	∑	∑	PROPN
ejpam-6138	32	4	l=0	l=0	PROPN
ejpam-6138	32	5	µ	µ	X
ejpam-6138	32	6	(	(	PUNCT
ejpam-6138	32	7	l)(θ	l)(θ	PROPN
ejpam-6138	32	8	)	)	PUNCT
ejpam-6138	32	9	l	l	NOUN
ejpam-6138	32	10	!	!	PUNCT
ejpam-6138	33	1	(	(	PUNCT
ejpam-6138	33	2	τ	τ	X
ejpam-6138	33	3	−	−	PROPN
ejpam-6138	33	4	θ)l])(τ	θ)l])(τ	PROPN
ejpam-6138	33	5	)	)	PUNCT
ejpam-6138	33	6	,	,	PUNCT
ejpam-6138	33	7	n	n	NOUN
ejpam-6138	33	8	=	=	SYM
ejpam-6138	34	1	[	[	X
ejpam-6138	34	2	re(σ	re(σ	X
ejpam-6138	34	3	)	)	PUNCT
ejpam-6138	34	4	]	]	PUNCT
ejpam-6138	34	5	.	.	PUNCT
ejpam-6138	35	1	(	(	PUNCT
ejpam-6138	35	2	2.3	2.3	NUM
ejpam-6138	35	3	)	)	PUNCT
ejpam-6138	35	4	lemma	lemma	PROPN
ejpam-6138	35	5	1	1	NUM
ejpam-6138	35	6	(	(	PUNCT
ejpam-6138	35	7	[	[	X
ejpam-6138	35	8	25	25	NUM
ejpam-6138	35	9	]	]	PUNCT
ejpam-6138	35	10	)	)	PUNCT
ejpam-6138	35	11	.	.	PUNCT
ejpam-6138	36	1	let	let	VERB
ejpam-6138	36	2	σ	σ	NOUN
ejpam-6138	36	3	,	,	PUNCT
ejpam-6138	36	4	ϱ	ϱ	ADP
ejpam-6138	36	5	>	>	X
ejpam-6138	36	6	0	0	NUM
ejpam-6138	36	7	and	and	CCONJ
ejpam-6138	36	8	µ	µ	PROPN
ejpam-6138	36	9	∈	∈	PROPN
ejpam-6138	36	10	c(j	c(j	NOUN
ejpam-6138	36	11	,	,	PUNCT
ejpam-6138	36	12	r	r	NOUN
ejpam-6138	36	13	)	)	PUNCT
ejpam-6138	36	14	∩	∩	ADJ
ejpam-6138	36	15	c1(j	c1(j	NOUN
ejpam-6138	36	16	,	,	PUNCT
ejpam-6138	36	17	r	r	NOUN
ejpam-6138	36	18	)	)	PUNCT
ejpam-6138	36	19	.	.	PUNCT
ejpam-6138	37	1	then	then	ADV
ejpam-6138	37	2	1	1	X
ejpam-6138	37	3	.	.	PUNCT
ejpam-6138	38	1	the	the	DET
ejpam-6138	38	2	caputo	caputo	PROPN
ejpam-6138	38	3	-	-	PUNCT
ejpam-6138	38	4	katugampola	katugampola	PROPN
ejpam-6138	38	5	fractional	fractional	ADJ
ejpam-6138	38	6	derivative	derivative	ADJ
ejpam-6138	38	7	differential	differential	NOUN
ejpam-6138	38	8	equation	equation	NOUN
ejpam-6138	38	9	ϱ	ϱ	ADP
ejpam-6138	38	10	cd	cd	PROPN
ejpam-6138	38	11	σ	σ	PROPN
ejpam-6138	38	12	θ+µ(τ	θ+µ(τ	PROPN
ejpam-6138	38	13	)	)	PUNCT
ejpam-6138	38	14	=	=	SYM
ejpam-6138	38	15	0	0	NUM
ejpam-6138	38	16	,	,	PUNCT
ejpam-6138	38	17	has	have	VERB
ejpam-6138	38	18	a	a	DET
ejpam-6138	38	19	solution	solution	NOUN
ejpam-6138	38	20	.	.	PUNCT
ejpam-6138	39	1	µ(τ	µ(τ	NOUN
ejpam-6138	39	2	)	)	PUNCT
ejpam-6138	39	3	=	=	SYM
ejpam-6138	39	4	p0	p0	NOUN
ejpam-6138	39	5	+	+	CCONJ
ejpam-6138	39	6	p1	p1	PROPN
ejpam-6138	39	7	(	(	PUNCT
ejpam-6138	39	8	τ	τ	PROPN
ejpam-6138	39	9	ϱ−θϱ	ϱ−θϱ	PROPN
ejpam-6138	39	10	ϱ	ϱ	PROPN
ejpam-6138	39	11	)	)	PUNCT
ejpam-6138	39	12	+	+	CCONJ
ejpam-6138	39	13	p2	p2	NOUN
ejpam-6138	39	14	(	(	PUNCT
ejpam-6138	39	15	τ	τ	PROPN
ejpam-6138	39	16	ϱ−θϱ	ϱ−θϱ	PROPN
ejpam-6138	39	17	ϱ	ϱ	PROPN
ejpam-6138	39	18	)	)	PUNCT
ejpam-6138	39	19	2	2	NUM
ejpam-6138	39	20	+	+	CCONJ
ejpam-6138	39	21	...	...	PUNCT
ejpam-6138	40	1	+	+	CCONJ
ejpam-6138	40	2	pn−1	pn−1	ADJ
ejpam-6138	40	3	(	(	PUNCT
ejpam-6138	40	4	τ	τ	PROPN
ejpam-6138	40	5	ϱ−θϱ	ϱ−θϱ	PROPN
ejpam-6138	40	6	ϱ	ϱ	PROPN
ejpam-6138	40	7	)	)	PUNCT
ejpam-6138	40	8	n−1	n−1	PROPN
ejpam-6138	40	9	,	,	PUNCT
ejpam-6138	40	10	where	where	SCONJ
ejpam-6138	40	11	pi	pi	NOUN
ejpam-6138	40	12	∈	∈	PROPN
ejpam-6138	40	13	r	r	PROPN
ejpam-6138	40	14	,	,	PUNCT
ejpam-6138	40	15	i	i	NOUN
ejpam-6138	40	16	=	=	NOUN
ejpam-6138	40	17	0	0	NUM
ejpam-6138	40	18	,	,	PUNCT
ejpam-6138	40	19	1	1	NUM
ejpam-6138	40	20	,	,	PUNCT
ejpam-6138	40	21	2	2	NUM
ejpam-6138	40	22	,	,	PUNCT
ejpam-6138	40	23	...	...	PUNCT
ejpam-6138	40	24	,	,	PUNCT
ejpam-6138	40	25	n	n	CCONJ
ejpam-6138	40	26	−	−	PROPN
ejpam-6138	40	27	1	1	NUM
ejpam-6138	40	28	and	and	CCONJ
ejpam-6138	40	29	n	n	NOUN
ejpam-6138	40	30	=	=	SYM
ejpam-6138	41	1	[	[	X
ejpam-6138	41	2	σ	σ	X
ejpam-6138	41	3	]	]	X
ejpam-6138	41	4	+	+	NUM
ejpam-6138	41	5	1	1	NUM
ejpam-6138	41	6	.	.	X
ejpam-6138	41	7	2	2	NUM
ejpam-6138	41	8	.	.	X
ejpam-6138	42	1	if	if	SCONJ
ejpam-6138	42	2	µ	µ	NUM
ejpam-6138	42	3	,	,	PUNCT
ejpam-6138	42	4	ϱ	ϱ	PROPN
ejpam-6138	42	5	cd	cd	PROPN
ejpam-6138	42	6	σ	σ	PROPN
ejpam-6138	42	7	θ+µ	θ+µ	PROPN
ejpam-6138	42	8	∈	∈	PROPN
ejpam-6138	42	9	c(j	c(j	NOUN
ejpam-6138	42	10	,	,	PUNCT
ejpam-6138	42	11	r	r	NOUN
ejpam-6138	42	12	)	)	PUNCT
ejpam-6138	42	13	∩	∩	ADJ
ejpam-6138	42	14	c1(j	c1(j	NOUN
ejpam-6138	42	15	,	,	PUNCT
ejpam-6138	42	16	r	r	NOUN
ejpam-6138	42	17	)	)	PUNCT
ejpam-6138	42	18	.	.	PUNCT
ejpam-6138	43	1	then	then	ADV
ejpam-6138	43	2	ϱ	ϱ	VERB
ejpam-6138	43	3	i	i	PROPN
ejpam-6138	43	4	σ	σ	X
ejpam-6138	43	5	θ+	θ+	PUNCT
ejpam-6138	43	6	ϱ	ϱ	PROPN
ejpam-6138	43	7	cd	cd	PROPN
ejpam-6138	43	8	σ	σ	PROPN
ejpam-6138	43	9	θ+µ(τ	θ+µ(τ	PROPN
ejpam-6138	43	10	)	)	PUNCT
ejpam-6138	43	11	=	=	SYM
ejpam-6138	43	12	µ(τ	µ(τ	PROPN
ejpam-6138	43	13	)	)	PUNCT
ejpam-6138	43	14	+	+	CCONJ
ejpam-6138	43	15	p0	p0	NOUN
ejpam-6138	43	16	+	+	CCONJ
ejpam-6138	43	17	p1	p1	PROPN
ejpam-6138	43	18	(	(	PUNCT
ejpam-6138	43	19	τ	τ	PROPN
ejpam-6138	43	20	ϱ−θϱ	ϱ−θϱ	PROPN
ejpam-6138	43	21	ϱ	ϱ	PROPN
ejpam-6138	43	22	)	)	PUNCT
ejpam-6138	43	23	+	+	CCONJ
ejpam-6138	43	24	p2	p2	NOUN
ejpam-6138	43	25	(	(	PUNCT
ejpam-6138	43	26	τ	τ	PROPN
ejpam-6138	43	27	ϱ−θϱ	ϱ−θϱ	PROPN
ejpam-6138	43	28	ϱ	ϱ	PROPN
ejpam-6138	43	29	)	)	PUNCT
ejpam-6138	43	30	2	2	NUM
ejpam-6138	43	31	+	+	CCONJ
ejpam-6138	43	32	...	...	PUNCT
ejpam-6138	44	1	+	+	CCONJ
ejpam-6138	44	2	pn−1	pn−1	ADJ
ejpam-6138	44	3	(	(	PUNCT
ejpam-6138	44	4	τ	τ	PROPN
ejpam-6138	44	5	ϱ−θϱ	ϱ−θϱ	PROPN
ejpam-6138	44	6	ϱ	ϱ	PROPN
ejpam-6138	44	7	)	)	PUNCT
ejpam-6138	44	8	n−1	n−1	PROPN
ejpam-6138	44	9	,	,	PUNCT
ejpam-6138	44	10	(	(	PUNCT
ejpam-6138	44	11	2.4	2.4	NUM
ejpam-6138	44	12	)	)	PUNCT
ejpam-6138	44	13	where	where	SCONJ
ejpam-6138	44	14	pi	pi	NOUN
ejpam-6138	44	15	∈	∈	PROPN
ejpam-6138	44	16	r	r	PROPN
ejpam-6138	44	17	,	,	PUNCT
ejpam-6138	44	18	i	i	NOUN
ejpam-6138	44	19	=	=	NOUN
ejpam-6138	44	20	0	0	NUM
ejpam-6138	44	21	,	,	PUNCT
ejpam-6138	44	22	1	1	NUM
ejpam-6138	44	23	,	,	PUNCT
ejpam-6138	44	24	2	2	NUM
ejpam-6138	44	25	,	,	PUNCT
ejpam-6138	44	26	...	...	PUNCT
ejpam-6138	44	27	,	,	PUNCT
ejpam-6138	44	28	n	n	CCONJ
ejpam-6138	44	29	−	−	PROPN
ejpam-6138	44	30	1	1	NUM
ejpam-6138	44	31	and	and	CCONJ
ejpam-6138	44	32	n	n	NOUN
ejpam-6138	44	33	=	=	SYM
ejpam-6138	45	1	[	[	X
ejpam-6138	45	2	σ	σ	X
ejpam-6138	45	3	]	]	X
ejpam-6138	45	4	+	+	NUM
ejpam-6138	45	5	1	1	NUM
ejpam-6138	45	6	.	.	X
ejpam-6138	45	7	3	3	NUM
ejpam-6138	45	8	.	.	X
ejpam-6138	45	9	main	main	ADJ
ejpam-6138	45	10	results	result	NOUN
ejpam-6138	45	11	at	at	ADP
ejpam-6138	45	12	the	the	DET
ejpam-6138	45	13	heart	heart	NOUN
ejpam-6138	45	14	of	of	ADP
ejpam-6138	45	15	this	this	DET
ejpam-6138	45	16	passage	passage	NOUN
ejpam-6138	45	17	,	,	PUNCT
ejpam-6138	45	18	we	we	PRON
ejpam-6138	45	19	witness	witness	VERB
ejpam-6138	45	20	significant	significant	ADJ
ejpam-6138	45	21	propositions	proposition	NOUN
ejpam-6138	45	22	and	and	CCONJ
ejpam-6138	45	23	theorems	theorem	NOUN
ejpam-6138	45	24	on	on	ADP
ejpam-6138	45	25	which	which	PRON
ejpam-6138	45	26	all	all	DET
ejpam-6138	45	27	this	this	DET
ejpam-6138	45	28	work	work	NOUN
ejpam-6138	45	29	is	be	AUX
ejpam-6138	45	30	based	base	VERB
ejpam-6138	45	31	.	.	PUNCT
ejpam-6138	46	1	we	we	PRON
ejpam-6138	46	2	give	give	VERB
ejpam-6138	46	3	the	the	DET
ejpam-6138	46	4	integral	integral	ADJ
ejpam-6138	46	5	formula	formula	NOUN
ejpam-6138	46	6	for	for	ADP
ejpam-6138	46	7	the	the	DET
ejpam-6138	46	8	generalized	generalize	VERB
ejpam-6138	46	9	fractional	fractional	ADJ
ejpam-6138	46	10	bvp	bvp	NOUN
ejpam-6138	46	11	(	(	PUNCT
ejpam-6138	46	12	1.4	1.4	NUM
ejpam-6138	46	13	)	)	PUNCT
ejpam-6138	46	14	from	from	ADP
ejpam-6138	46	15	the	the	DET
ejpam-6138	46	16	principle	principle	NOUN
ejpam-6138	46	17	of	of	ADP
ejpam-6138	46	18	the	the	DET
ejpam-6138	46	19	green	green	ADJ
ejpam-6138	46	20	function	function	NOUN
ejpam-6138	46	21	.	.	PUNCT
ejpam-6138	47	1	lemma	lemma	PROPN
ejpam-6138	47	2	2	2	X
ejpam-6138	47	3	.	.	X
ejpam-6138	47	4	presume	presume	VERB
ejpam-6138	47	5	that	that	SCONJ
ejpam-6138	47	6	ξ	ξ	PROPN
ejpam-6138	47	7	is	be	AUX
ejpam-6138	47	8	a	a	DET
ejpam-6138	47	9	function	function	NOUN
ejpam-6138	47	10	is	be	AUX
ejpam-6138	47	11	continuous	continuous	ADJ
ejpam-6138	47	12	and	and	CCONJ
ejpam-6138	47	13	either	either	CCONJ
ejpam-6138	47	14	a	a	DET
ejpam-6138	47	15	function	function	NOUN
ejpam-6138	47	16	µ	µ	PRON
ejpam-6138	47	17	∈	∈	PROPN
ejpam-6138	47	18	c[θ	c[θ	PROPN
ejpam-6138	47	19	,	,	PUNCT
ejpam-6138	47	20	ϑ	ϑ	X
ejpam-6138	47	21	]	]	X
ejpam-6138	47	22	is	be	AUX
ejpam-6138	47	23	a	a	DET
ejpam-6138	47	24	solution	solution	NOUN
ejpam-6138	47	25	of	of	ADP
ejpam-6138	47	26	(	(	PUNCT
ejpam-6138	47	27	1.4	1.4	NUM
ejpam-6138	47	28	)	)	PUNCT
ejpam-6138	47	29	equivalent	equivalent	NOUN
ejpam-6138	47	30	that	that	SCONJ
ejpam-6138	47	31	µ	µ	ADJ
ejpam-6138	47	32	check	check	VERB
ejpam-6138	47	33	the	the	DET
ejpam-6138	47	34	integral	integral	ADJ
ejpam-6138	47	35	equation	equation	NOUN
ejpam-6138	47	36	µ(τ	µ(τ	NOUN
ejpam-6138	47	37	)	)	PUNCT
ejpam-6138	47	38	=	=	PUNCT
ejpam-6138	48	1	[	[	X
ejpam-6138	48	2	(	(	PUNCT
ejpam-6138	48	3	λ2	λ2	NOUN
ejpam-6138	48	4	−	−	PROPN
ejpam-6138	48	5	λ1	λ1	PROPN
ejpam-6138	48	6	)	)	PUNCT
ejpam-6138	48	7	(	(	PUNCT
ejpam-6138	48	8	τ	τ	PROPN
ejpam-6138	48	9	ϱ−θϱ	ϱ−θϱ	PROPN
ejpam-6138	48	10	)	)	PUNCT
ejpam-6138	48	11	(	(	PUNCT
ejpam-6138	48	12	ϑϱ−θϱ	ϑϱ−θϱ	ADV
ejpam-6138	48	13	)	)	PUNCT
ejpam-6138	49	1	+	+	SYM
ejpam-6138	49	2	λ1	λ1	ADJ
ejpam-6138	49	3	]	]	X
ejpam-6138	50	1	+	+	NUM
ejpam-6138	50	2	∫	∫	PROPN
ejpam-6138	50	3	ϑ	ϑ	X
ejpam-6138	50	4	θ	θ	PROPN
ejpam-6138	50	5	h̵(τ	h̵(τ	PROPN
ejpam-6138	50	6	,	,	PUNCT
ejpam-6138	50	7	r	r	NOUN
ejpam-6138	50	8	)	)	PUNCT
ejpam-6138	50	9	ξ	ξ	PROPN
ejpam-6138	50	10	(	(	PUNCT
ejpam-6138	50	11	r	r	NOUN
ejpam-6138	50	12	,	,	PUNCT
ejpam-6138	50	13	µ(r	µ(r	NOUN
ejpam-6138	50	14	)	)	PUNCT
ejpam-6138	50	15	,	,	PUNCT
ejpam-6138	50	16	ϱcdς	ϱcdς	ADJ
ejpam-6138	50	17	θ+µ(r	θ+µ(r	NOUN
ejpam-6138	50	18	)	)	PUNCT
ejpam-6138	50	19	)	)	PUNCT
ejpam-6138	50	20	dr	dr	PROPN
ejpam-6138	50	21	,	,	PUNCT
ejpam-6138	50	22	(	(	PUNCT
ejpam-6138	50	23	3.1	3.1	NUM
ejpam-6138	50	24	)	)	PUNCT
ejpam-6138	50	25	where	where	SCONJ
ejpam-6138	50	26	for	for	ADP
ejpam-6138	50	27	r	r	NOUN
ejpam-6138	50	28	,	,	PUNCT
ejpam-6138	50	29	τ	τ	PROPN
ejpam-6138	50	30	∈	∈	PROPN
ejpam-6138	51	1	[	[	X
ejpam-6138	51	2	θ	θ	X
ejpam-6138	51	3	,	,	PUNCT
ejpam-6138	51	4	ϑ	ϑ	X
ejpam-6138	51	5	]	]	X
ejpam-6138	51	6	,	,	PUNCT
ejpam-6138	51	7	h̵(τ	h̵(τ	PROPN
ejpam-6138	51	8	,	,	PUNCT
ejpam-6138	51	9	r	r	NOUN
ejpam-6138	51	10	)	)	PUNCT
ejpam-6138	51	11	=	=	PUNCT
ejpam-6138	51	12	ϱ	ϱ	ADP
ejpam-6138	51	13	1−σ	1−σ	NUM
ejpam-6138	51	14	γ(σ	γ(σ	PROPN
ejpam-6138	51	15	)	)	PUNCT
ejpam-6138	51	16	⎧⎪⎪⎪⎨⎪⎪⎪⎩	⎧⎪⎪⎪⎨⎪⎪⎪⎩	PROPN
ejpam-6138	51	17	(	(	PUNCT
ejpam-6138	51	18	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	51	19	)	)	PUNCT
ejpam-6138	51	20	(	(	PUNCT
ejpam-6138	51	21	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-6138	51	22	)	)	PUNCT
ejpam-6138	51	23	r	r	NOUN
ejpam-6138	51	24	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-6138	51	25	−	−	NOUN
ejpam-6138	51	26	r	r	NOUN
ejpam-6138	51	27	ϱ)σ−1	ϱ)σ−1	NOUN
ejpam-6138	51	28	−	−	PROPN
ejpam-6138	51	29	r	r	NOUN
ejpam-6138	52	1	ϱ−1(τϱ	ϱ−1(τϱ	PROPN
ejpam-6138	52	2	−	−	NOUN
ejpam-6138	52	3	r	r	NOUN
ejpam-6138	52	4	ϱ)σ−1	ϱ)σ−1	NOUN
ejpam-6138	52	5	,	,	PUNCT
ejpam-6138	52	6	r	r	NOUN
ejpam-6138	52	7	≤	≤	NUM
ejpam-6138	52	8	τ	τ	X
ejpam-6138	52	9	,	,	PUNCT
ejpam-6138	52	10	(	(	PUNCT
ejpam-6138	52	11	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	52	12	)	)	PUNCT
ejpam-6138	52	13	(	(	PUNCT
ejpam-6138	52	14	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-6138	52	15	)	)	PUNCT
ejpam-6138	52	16	r	r	NOUN
ejpam-6138	52	17	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-6138	53	1	−	−	NOUN
ejpam-6138	53	2	r	r	NOUN
ejpam-6138	53	3	ϱ)σ−1	ϱ)σ−1	NOUN
ejpam-6138	53	4	,	,	PUNCT
ejpam-6138	53	5	τ	τ	PROPN
ejpam-6138	53	6	≤	≤	PROPN
ejpam-6138	53	7	r.	r.	X
ejpam-6138	53	8	(	(	PUNCT
ejpam-6138	53	9	3.2	3.2	NUM
ejpam-6138	53	10	)	)	PUNCT
ejpam-6138	53	11	z.	z.	PROPN
ejpam-6138	53	12	bekri	bekri	PROPN
ejpam-6138	53	13	et	et	PROPN
ejpam-6138	53	14	al	al	PROPN
ejpam-6138	53	15	.	.	PUNCT
ejpam-6138	53	16	/	/	SYM
ejpam-6138	53	17	eur	eur	PROPN
ejpam-6138	53	18	.	.	PUNCT
ejpam-6138	54	1	j.	j.	PROPN
ejpam-6138	54	2	pure	pure	PROPN
ejpam-6138	54	3	appl	appl	PROPN
ejpam-6138	54	4	.	.	PROPN
ejpam-6138	54	5	math	math	PROPN
ejpam-6138	54	6	,	,	PUNCT
ejpam-6138	54	7	18	18	NUM
ejpam-6138	54	8	(	(	PUNCT
ejpam-6138	54	9	2	2	NUM
ejpam-6138	54	10	)	)	PUNCT
ejpam-6138	54	11	(	(	PUNCT
ejpam-6138	54	12	2025	2025	NUM
ejpam-6138	54	13	)	)	PUNCT
ejpam-6138	54	14	,	,	PUNCT
ejpam-6138	54	15	6138	6138	NUM
ejpam-6138	54	16	4	4	NUM
ejpam-6138	54	17	of	of	ADP
ejpam-6138	54	18	17	17	NUM
ejpam-6138	54	19	proof	proof	NOUN
ejpam-6138	54	20	.	.	PUNCT
ejpam-6138	55	1	by	by	ADP
ejpam-6138	55	2	the	the	DET
ejpam-6138	55	3	lemma(1),we	lemma(1),we	NOUN
ejpam-6138	55	4	solve	solve	NOUN
ejpam-6138	55	5	this	this	DET
ejpam-6138	55	6	problem	problem	NOUN
ejpam-6138	55	7	ϱ	ϱ	ADP
ejpam-6138	55	8	cd	cd	PROPN
ejpam-6138	55	9	σ	σ	PROPN
ejpam-6138	55	10	θ+µ(τ	θ+µ(τ	PROPN
ejpam-6138	55	11	)	)	PUNCT
ejpam-6138	55	12	=	=	SYM
ejpam-6138	55	13	−q(τ	−q(τ	NOUN
ejpam-6138	55	14	)	)	PUNCT
ejpam-6138	55	15	.	.	PUNCT
ejpam-6138	56	1	according	accord	VERB
ejpam-6138	56	2	to	to	ADP
ejpam-6138	56	3	(	(	PUNCT
ejpam-6138	56	4	2.4	2.4	NUM
ejpam-6138	56	5	)	)	PUNCT
ejpam-6138	56	6	,	,	PUNCT
ejpam-6138	56	7	we	we	PRON
ejpam-6138	56	8	obtain	obtain	VERB
ejpam-6138	56	9	ϱ	ϱ	ADP
ejpam-6138	56	10	i	i	PROPN
ejpam-6138	56	11	σ	σ	X
ejpam-6138	56	12	θ+	θ+	PUNCT
ejpam-6138	56	13	ϱ	ϱ	PROPN
ejpam-6138	56	14	cd	cd	PROPN
ejpam-6138	56	15	σ	σ	PROPN
ejpam-6138	56	16	θ+µ(τ	θ+µ(τ	PROPN
ejpam-6138	56	17	)	)	PUNCT
ejpam-6138	56	18	=	=	SYM
ejpam-6138	56	19	−	−	PROPN
ejpam-6138	56	20	ϱ	ϱ	VERB
ejpam-6138	56	21	i	i	PROPN
ejpam-6138	56	22	σ	σ	NOUN
ejpam-6138	56	23	θ+q(τ	θ+q(τ	ADV
ejpam-6138	56	24	)	)	PUNCT
ejpam-6138	57	1	+	+	CCONJ
ejpam-6138	57	2	p0	p0	NOUN
ejpam-6138	57	3	+	+	CCONJ
ejpam-6138	57	4	p1	p1	PROPN
ejpam-6138	57	5	(	(	PUNCT
ejpam-6138	57	6	τϱ	τϱ	ADP
ejpam-6138	57	7	−	−	PROPN
ejpam-6138	57	8	θ	θ	PROPN
ejpam-6138	57	9	ϱ	ϱ	NOUN
ejpam-6138	57	10	)	)	PUNCT
ejpam-6138	57	11	ϱ	ϱ	ADP
ejpam-6138	57	12	µ(τ	µ(τ	NOUN
ejpam-6138	57	13	)	)	PUNCT
ejpam-6138	57	14	=	=	SYM
ejpam-6138	58	1	−	−	PROPN
ejpam-6138	58	2	ϱ	ϱ	VERB
ejpam-6138	58	3	i	i	PROPN
ejpam-6138	58	4	σ	σ	NOUN
ejpam-6138	58	5	θ+q(τ	θ+q(τ	ADV
ejpam-6138	58	6	)	)	PUNCT
ejpam-6138	58	7	+	+	CCONJ
ejpam-6138	58	8	p0	p0	NOUN
ejpam-6138	58	9	+	+	CCONJ
ejpam-6138	58	10	p1	p1	PROPN
ejpam-6138	58	11	(	(	PUNCT
ejpam-6138	58	12	τϱ	τϱ	ADP
ejpam-6138	58	13	−	−	PROPN
ejpam-6138	58	14	θ	θ	PROPN
ejpam-6138	58	15	ϱ	ϱ	NOUN
ejpam-6138	58	16	)	)	PUNCT
ejpam-6138	58	17	ϱ	ϱ	ADP
ejpam-6138	58	18	µ(τ	µ(τ	PROPN
ejpam-6138	58	19	)	)	PUNCT
ejpam-6138	58	20	=	=	SYM
ejpam-6138	58	21	−ϱ	−ϱ	NOUN
ejpam-6138	58	22	1−σ	1−σ	NUM
ejpam-6138	59	1	γ(σ	γ(σ	ADJ
ejpam-6138	59	2	)	)	PUNCT
ejpam-6138	59	3	∫	∫	PROPN
ejpam-6138	60	1	τ	τ	PROPN
ejpam-6138	60	2	θ	θ	PROPN
ejpam-6138	60	3	r	r	NOUN
ejpam-6138	60	4	ϱ−1(τϱ	ϱ−1(τϱ	PROPN
ejpam-6138	60	5	−	−	NOUN
ejpam-6138	60	6	r	r	NOUN
ejpam-6138	60	7	ϱ)σ−1q(r)dr	ϱ)σ−1q(r)dr	NOUN
ejpam-6138	60	8	+	+	CCONJ
ejpam-6138	60	9	p0	p0	NOUN
ejpam-6138	60	10	+	+	CCONJ
ejpam-6138	60	11	p1	p1	PROPN
ejpam-6138	60	12	(	(	PUNCT
ejpam-6138	60	13	τϱ−θϱ	τϱ−θϱ	NOUN
ejpam-6138	60	14	)	)	PUNCT
ejpam-6138	60	15	ϱ	ϱ	NOUN
ejpam-6138	60	16	,	,	PUNCT
ejpam-6138	60	17	by	by	ADP
ejpam-6138	60	18	using	use	VERB
ejpam-6138	60	19	boundary	boundary	ADJ
ejpam-6138	60	20	conditions	condition	NOUN
ejpam-6138	60	21	µ(θ	µ(θ	ADJ
ejpam-6138	60	22	)	)	PUNCT
ejpam-6138	61	1	=	=	SYM
ejpam-6138	61	2	λ1	λ1	ADJ
ejpam-6138	61	3	⟹	⟹	NUM
ejpam-6138	61	4	p0	p0	NOUN
ejpam-6138	61	5	=	=	SYM
ejpam-6138	61	6	λ1	λ1	PROPN
ejpam-6138	61	7	,	,	PUNCT
ejpam-6138	61	8	µ(ϑ	µ(ϑ	PROPN
ejpam-6138	61	9	)	)	PUNCT
ejpam-6138	61	10	=	=	SYM
ejpam-6138	61	11	λ2	λ2	NOUN
ejpam-6138	61	12	⟹	⟹	NUM
ejpam-6138	61	13	p1	p1	NOUN
ejpam-6138	61	14	=	=	PUNCT
ejpam-6138	61	15	ϱ(λ2−λ1	ϱ(λ2−λ1	NOUN
ejpam-6138	61	16	)	)	PUNCT
ejpam-6138	61	17	(	(	PUNCT
ejpam-6138	61	18	ϑϱ−θϱ	ϑϱ−θϱ	ADV
ejpam-6138	61	19	)	)	PUNCT
ejpam-6138	62	1	+	+	CCONJ
ejpam-6138	62	2	ϱ	ϱ	ADP
ejpam-6138	62	3	2−σ	2−σ	NUM
ejpam-6138	62	4	(	(	PUNCT
ejpam-6138	62	5	ϑϱ−θϱ)γ(σ	ϑϱ−θϱ)γ(σ	PROPN
ejpam-6138	62	6	)	)	PUNCT
ejpam-6138	62	7	∫	∫	PROPN
ejpam-6138	62	8	ϑ	ϑ	X
ejpam-6138	62	9	θ	θ	PROPN
ejpam-6138	62	10	r	r	NOUN
ejpam-6138	62	11	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-6138	62	12	−	−	NOUN
ejpam-6138	62	13	r	r	NOUN
ejpam-6138	62	14	ϱ)σ−1q(r	ϱ)σ−1q(r	NOUN
ejpam-6138	62	15	)	)	PUNCT
ejpam-6138	62	16	dr	dr	PROPN
ejpam-6138	62	17	.	.	PROPN
ejpam-6138	63	1	by	by	ADP
ejpam-6138	63	2	replacing	replace	VERB
ejpam-6138	63	3	in	in	ADP
ejpam-6138	63	4	µ(τ	µ(τ	NOUN
ejpam-6138	63	5	)	)	PUNCT
ejpam-6138	63	6	,	,	PUNCT
ejpam-6138	63	7	we	we	PRON
ejpam-6138	63	8	get	get	VERB
ejpam-6138	63	9	µ(τ	µ(τ	NOUN
ejpam-6138	63	10	)	)	PUNCT
ejpam-6138	63	11	=	=	SYM
ejpam-6138	63	12	−ϱ	−ϱ	NOUN
ejpam-6138	63	13	1−σ	1−σ	NUM
ejpam-6138	64	1	γ(σ	γ(σ	ADJ
ejpam-6138	64	2	)	)	PUNCT
ejpam-6138	64	3	∫	∫	PROPN
ejpam-6138	65	1	τ	τ	PROPN
ejpam-6138	65	2	θ	θ	PROPN
ejpam-6138	65	3	r	r	NOUN
ejpam-6138	65	4	ϱ−1(τϱ	ϱ−1(τϱ	PROPN
ejpam-6138	65	5	−	−	NOUN
ejpam-6138	65	6	r	r	NOUN
ejpam-6138	65	7	ϱ)σ−1q(r)dr	ϱ)σ−1q(r)dr	NOUN
ejpam-6138	65	8	+	+	CCONJ
ejpam-6138	65	9	[	[	PUNCT
ejpam-6138	65	10	ϱ(λ2	ϱ(λ2	ADV
ejpam-6138	65	11	−	−	PROPN
ejpam-6138	65	12	λ1	λ1	PROPN
ejpam-6138	65	13	)	)	PUNCT
ejpam-6138	65	14	+	+	CCONJ
ejpam-6138	65	15	ϱ	ϱ	ADP
ejpam-6138	65	16	2−σ	2−σ	NUM
ejpam-6138	65	17	γ(σ	γ(σ	PROPN
ejpam-6138	65	18	)	)	PUNCT
ejpam-6138	65	19	∫	∫	PROPN
ejpam-6138	65	20	ϑ	ϑ	X
ejpam-6138	65	21	θ	θ	PROPN
ejpam-6138	65	22	r	r	NOUN
ejpam-6138	65	23	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-6138	65	24	−	−	NOUN
ejpam-6138	65	25	r	r	NOUN
ejpam-6138	65	26	ϱ)σ−1q(r)dr	ϱ)σ−1q(r)dr	NOUN
ejpam-6138	65	27	]	]	PUNCT
ejpam-6138	65	28	(	(	PUNCT
ejpam-6138	65	29	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	65	30	)	)	PUNCT
ejpam-6138	65	31	(	(	PUNCT
ejpam-6138	65	32	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-6138	65	33	)	)	PUNCT
ejpam-6138	66	1	+	+	CCONJ
ejpam-6138	66	2	λ1	λ1	ADJ
ejpam-6138	66	3	,	,	PUNCT
ejpam-6138	66	4	and	and	CCONJ
ejpam-6138	66	5	µ(τ	µ(τ	PROPN
ejpam-6138	66	6	)	)	PUNCT
ejpam-6138	66	7	=	=	SYM
ejpam-6138	66	8	−ϱ	−ϱ	NOUN
ejpam-6138	66	9	1−σ	1−σ	NUM
ejpam-6138	67	1	γ(σ	γ(σ	ADJ
ejpam-6138	67	2	)	)	PUNCT
ejpam-6138	67	3	∫	∫	PROPN
ejpam-6138	68	1	τ	τ	PROPN
ejpam-6138	68	2	θ	θ	PROPN
ejpam-6138	68	3	r	r	NOUN
ejpam-6138	69	1	ϱ−1(τϱ	ϱ−1(τϱ	PROPN
ejpam-6138	69	2	−	−	NOUN
ejpam-6138	69	3	r	r	NOUN
ejpam-6138	69	4	ϱ)σ−1q(r	ϱ)σ−1q(r	NOUN
ejpam-6138	69	5	)	)	PUNCT
ejpam-6138	70	1	dr	dr	PROPN
ejpam-6138	70	2	+	+	CCONJ
ejpam-6138	70	3	ϱ	ϱ	PROPN
ejpam-6138	70	4	1−σ(τϱ−θϱ	1−σ(τϱ−θϱ	NUM
ejpam-6138	70	5	)	)	PUNCT
ejpam-6138	70	6	(	(	PUNCT
ejpam-6138	70	7	ϑϱ−θϱ)γ(σ	ϑϱ−θϱ)γ(σ	PROPN
ejpam-6138	70	8	)	)	PUNCT
ejpam-6138	70	9	∫	∫	PROPN
ejpam-6138	71	1	ϑ	ϑ	X
ejpam-6138	71	2	θ	θ	PROPN
ejpam-6138	71	3	r	r	NOUN
ejpam-6138	71	4	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-6138	71	5	−	−	NOUN
ejpam-6138	71	6	r	r	NOUN
ejpam-6138	71	7	ϱ)σ−1q(r)dr	ϱ)σ−1q(r)dr	NOUN
ejpam-6138	71	8	+	+	CCONJ
ejpam-6138	71	9	(	(	PUNCT
ejpam-6138	71	10	λ2	λ2	NOUN
ejpam-6138	71	11	−	−	PROPN
ejpam-6138	71	12	λ1	λ1	PROPN
ejpam-6138	71	13	)	)	PUNCT
ejpam-6138	71	14	(	(	PUNCT
ejpam-6138	71	15	τ	τ	PROPN
ejpam-6138	71	16	ϱ−θϱ	ϱ−θϱ	PROPN
ejpam-6138	71	17	)	)	PUNCT
ejpam-6138	71	18	(	(	PUNCT
ejpam-6138	71	19	ϑϱ−θϱ	ϑϱ−θϱ	ADV
ejpam-6138	71	20	)	)	PUNCT
ejpam-6138	72	1	+	+	SYM
ejpam-6138	72	2	λ1	λ1	ADJ
ejpam-6138	72	3	.	.	PUNCT
ejpam-6138	73	1	therefore	therefore	ADV
ejpam-6138	73	2	,	,	PUNCT
ejpam-6138	73	3	µ(τ	µ(τ	PROPN
ejpam-6138	73	4	)	)	PUNCT
ejpam-6138	73	5	=	=	PUNCT
ejpam-6138	74	1	[	[	X
ejpam-6138	74	2	(	(	PUNCT
ejpam-6138	74	3	λ2	λ2	NOUN
ejpam-6138	74	4	−	−	PROPN
ejpam-6138	74	5	λ1	λ1	PROPN
ejpam-6138	74	6	)	)	PUNCT
ejpam-6138	74	7	(	(	PUNCT
ejpam-6138	74	8	τ	τ	PROPN
ejpam-6138	74	9	ϱ−θϱ	ϱ−θϱ	PROPN
ejpam-6138	74	10	)	)	PUNCT
ejpam-6138	74	11	(	(	PUNCT
ejpam-6138	74	12	ϑϱ−θϱ	ϑϱ−θϱ	ADV
ejpam-6138	74	13	)	)	PUNCT
ejpam-6138	75	1	+	+	SYM
ejpam-6138	75	2	λ1	λ1	ADJ
ejpam-6138	75	3	]	]	X
ejpam-6138	75	4	+	+	CCONJ
ejpam-6138	75	5	ϱ	ϱ	ADP
ejpam-6138	75	6	1−σ	1−σ	NUM
ejpam-6138	75	7	γ(σ	γ(σ	PROPN
ejpam-6138	75	8	)	)	PUNCT
ejpam-6138	75	9	∫	∫	PROPN
ejpam-6138	75	10	τ	τ	PROPN
ejpam-6138	75	11	θ	θ	PROPN
ejpam-6138	75	12	(	(	PUNCT
ejpam-6138	75	13	(	(	PUNCT
ejpam-6138	75	14	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	75	15	)	)	PUNCT
ejpam-6138	75	16	(	(	PUNCT
ejpam-6138	75	17	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-6138	75	18	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-6138	75	19	−	−	NOUN
ejpam-6138	75	20	r	r	NOUN
ejpam-6138	75	21	ϱ)σ−1	ϱ)σ−1	NOUN
ejpam-6138	75	22	−	−	PROPN
ejpam-6138	75	23	r	r	NOUN
ejpam-6138	76	1	ϱ−1(τϱ	ϱ−1(τϱ	PROPN
ejpam-6138	76	2	−	−	NOUN
ejpam-6138	76	3	r	r	NOUN
ejpam-6138	76	4	ϱ)σ−1	ϱ)σ−1	NOUN
ejpam-6138	76	5	)	)	PUNCT
ejpam-6138	76	6	q(r)dr	q(r)dr	VERB
ejpam-6138	76	7	+	+	X
ejpam-6138	76	8	ϱ	ϱ	ADP
ejpam-6138	76	9	1−σ	1−σ	NUM
ejpam-6138	76	10	γ(σ	γ(σ	PROPN
ejpam-6138	76	11	)	)	PUNCT
ejpam-6138	76	12	∫	∫	PROPN
ejpam-6138	76	13	ϑ	ϑ	X
ejpam-6138	76	14	τ	τ	X
ejpam-6138	76	15	(	(	PUNCT
ejpam-6138	76	16	τϱ−θϱ	τϱ−θϱ	PROPN
ejpam-6138	76	17	)	)	PUNCT
ejpam-6138	76	18	(	(	PUNCT
ejpam-6138	76	19	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-6138	76	20	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-6138	76	21	−	−	NOUN
ejpam-6138	76	22	r	r	NOUN
ejpam-6138	76	23	ϱ)σ−1q(r)dr	ϱ)σ−1q(r)dr	NOUN
ejpam-6138	76	24	,	,	PUNCT
ejpam-6138	76	25	thus	thus	ADV
ejpam-6138	76	26	the	the	DET
ejpam-6138	76	27	proof	proof	NOUN
ejpam-6138	76	28	is	be	AUX
ejpam-6138	76	29	complete	complete	ADJ
ejpam-6138	76	30	.	.	PUNCT
ejpam-6138	77	1	immediately	immediately	ADV
ejpam-6138	77	2	,	,	PUNCT
ejpam-6138	77	3	we	we	PRON
ejpam-6138	77	4	will	will	AUX
ejpam-6138	77	5	present	present	VERB
ejpam-6138	77	6	the	the	DET
ejpam-6138	77	7	important	important	ADJ
ejpam-6138	77	8	salient	salient	NOUN
ejpam-6138	77	9	rules	rule	NOUN
ejpam-6138	77	10	that	that	PRON
ejpam-6138	77	11	will	will	AUX
ejpam-6138	77	12	make	make	VERB
ejpam-6138	77	13	it	it	PRON
ejpam-6138	77	14	easier	easy	ADJ
ejpam-6138	77	15	for	for	SCONJ
ejpam-6138	77	16	us	we	PRON
ejpam-6138	77	17	to	to	PART
ejpam-6138	77	18	achieve	achieve	VERB
ejpam-6138	77	19	our	our	PRON
ejpam-6138	77	20	desired	desire	VERB
ejpam-6138	77	21	objectives	objective	NOUN
ejpam-6138	77	22	.	.	PUNCT
ejpam-6138	78	1	z.	z.	PROPN
ejpam-6138	78	2	bekri	bekri	PROPN
ejpam-6138	78	3	et	et	PROPN
ejpam-6138	78	4	al	al	PROPN
ejpam-6138	78	5	.	.	PUNCT
ejpam-6138	78	6	/	/	SYM
ejpam-6138	78	7	eur	eur	PROPN
ejpam-6138	78	8	.	.	PUNCT
ejpam-6138	79	1	j.	j.	PROPN
ejpam-6138	79	2	pure	pure	PROPN
ejpam-6138	79	3	appl	appl	PROPN
ejpam-6138	79	4	.	.	PROPN
ejpam-6138	79	5	math	math	PROPN
ejpam-6138	79	6	,	,	PUNCT
ejpam-6138	79	7	18	18	NUM
ejpam-6138	79	8	(	(	PUNCT
ejpam-6138	79	9	2	2	NUM
ejpam-6138	79	10	)	)	PUNCT
ejpam-6138	79	11	(	(	PUNCT
ejpam-6138	79	12	2025	2025	NUM
ejpam-6138	79	13	)	)	PUNCT
ejpam-6138	79	14	,	,	PUNCT
ejpam-6138	79	15	6138	6138	NUM
ejpam-6138	79	16	5	5	NUM
ejpam-6138	79	17	of	of	ADP
ejpam-6138	79	18	17	17	NUM
ejpam-6138	79	19	proposition	proposition	NOUN
ejpam-6138	79	20	1	1	NUM
ejpam-6138	79	21	.	.	PUNCT
ejpam-6138	80	1	depending	depend	VERB
ejpam-6138	80	2	on	on	ADP
ejpam-6138	80	3	the	the	DET
ejpam-6138	80	4	green	green	ADJ
ejpam-6138	80	5	function	function	NOUN
ejpam-6138	80	6	h̵	h̵	PROPN
ejpam-6138	80	7	is	be	AUX
ejpam-6138	80	8	given	give	VERB
ejpam-6138	80	9	in	in	ADP
ejpam-6138	80	10	lemma	lemma	PROPN
ejpam-6138	80	11	2	2	NUM
ejpam-6138	80	12	.	.	PUNCT
ejpam-6138	81	1	therefore	therefore	ADV
ejpam-6138	81	2	∫	∫	PROPN
ejpam-6138	81	3	ϑ	ϑ	X
ejpam-6138	81	4	θ	θ	PROPN
ejpam-6138	81	5	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	81	6	,	,	PUNCT
ejpam-6138	81	7	r)∣	r)∣	PROPN
ejpam-6138	81	8	dr	dr	PROPN
ejpam-6138	81	9	≤	≤	PROPN
ejpam-6138	81	10	1	1	NUM
ejpam-6138	81	11	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	81	12	)	)	PUNCT
ejpam-6138	82	1	[	[	X
ejpam-6138	82	2	(	(	PUNCT
ejpam-6138	82	3	ϑ	ϑ	X
ejpam-6138	82	4	ϱ	ϱ	ADP
ejpam-6138	82	5	−	−	PROPN
ejpam-6138	82	6	θ	θ	NOUN
ejpam-6138	82	7	ϱ)σ−1(τϱ	ϱ)σ−1(τϱ	NOUN
ejpam-6138	82	8	−	−	NUM
ejpam-6138	82	9	θ	θ	PROPN
ejpam-6138	82	10	ϱ	ϱ	NOUN
ejpam-6138	82	11	)	)	PUNCT
ejpam-6138	82	12	−	−	PROPN
ejpam-6138	82	13	(	(	PUNCT
ejpam-6138	82	14	τϱ	τϱ	ADP
ejpam-6138	82	15	−	−	PROPN
ejpam-6138	82	16	θ	θ	PROPN
ejpam-6138	82	17	ϱ)σ	ϱ)σ	NOUN
ejpam-6138	82	18	]	]	PUNCT
ejpam-6138	82	19	,	,	PUNCT
ejpam-6138	82	20	(	(	PUNCT
ejpam-6138	82	21	3.3	3.3	NUM
ejpam-6138	82	22	)	)	PUNCT
ejpam-6138	82	23	and	and	CCONJ
ejpam-6138	82	24	∫	∫	PROPN
ejpam-6138	82	25	ϑ	ϑ	PROPN
ejpam-6138	82	26	θ	θ	PROPN
ejpam-6138	82	27	∂∣h̵(τ	∂∣h̵(τ	PROPN
ejpam-6138	82	28	,	,	PUNCT
ejpam-6138	82	29	r)∣	r)∣	PROPN
ejpam-6138	82	30	∂τ	∂τ	PROPN
ejpam-6138	82	31	dr	dr	PROPN
ejpam-6138	82	32	≤	≤	PROPN
ejpam-6138	82	33	1	1	NUM
ejpam-6138	82	34	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	NOUN
ejpam-6138	82	35	)	)	PUNCT
ejpam-6138	83	1	[	[	X
ejpam-6138	83	2	(	(	PUNCT
ejpam-6138	83	3	ϑ	ϑ	X
ejpam-6138	83	4	ϱ	ϱ	ADP
ejpam-6138	83	5	−	−	PROPN
ejpam-6138	83	6	θ	θ	PROPN
ejpam-6138	83	7	ϱ)σ−1τϱ−1	ϱ)σ−1τϱ−1	NOUN
ejpam-6138	83	8	−	−	PROPN
ejpam-6138	84	1	σ(τϱ	σ(τϱ	DET
ejpam-6138	84	2	−	−	NOUN
ejpam-6138	84	3	θ	θ	NOUN
ejpam-6138	84	4	ϱ)σ−1τϱ−1	ϱ)σ−1τϱ−1	NOUN
ejpam-6138	84	5	]	]	PUNCT
ejpam-6138	84	6	.	.	PUNCT
ejpam-6138	85	1	(	(	PUNCT
ejpam-6138	85	2	3.4	3.4	NUM
ejpam-6138	85	3	)	)	PUNCT
ejpam-6138	85	4	proof	proof	NOUN
ejpam-6138	85	5	.	.	PUNCT
ejpam-6138	86	1	we	we	PRON
ejpam-6138	86	2	determine	determine	VERB
ejpam-6138	86	3	∫	∫	PROPN
ejpam-6138	86	4	θ	θ	PROPN
ejpam-6138	86	5	ϑ	ϑ	PROPN
ejpam-6138	86	6	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	86	7	,	,	PUNCT
ejpam-6138	86	8	r)∣	r)∣	PROPN
ejpam-6138	86	9	dr	dr	PROPN
ejpam-6138	86	10	,	,	PUNCT
ejpam-6138	86	11	h̵(τ	h̵(τ	PROPN
ejpam-6138	86	12	,	,	PUNCT
ejpam-6138	86	13	r	r	NOUN
ejpam-6138	86	14	)	)	PUNCT
ejpam-6138	86	15	≥	≥	NOUN
ejpam-6138	86	16	0	0	NUM
ejpam-6138	86	17	.	.	NOUN
ejpam-6138	86	18	∀	∀	NUM
ejpam-6138	87	1	θ	θ	NOUN
ejpam-6138	87	2	≤	≤	NUM
ejpam-6138	87	3	τ	τ	X
ejpam-6138	87	4	,	,	PUNCT
ejpam-6138	87	5	r	r	NOUN
ejpam-6138	87	6	≤	≤	ADJ
ejpam-6138	87	7	ϑ.	ϑ.	NOUN
ejpam-6138	87	8	(	(	PUNCT
ejpam-6138	87	9	3.5	3.5	NUM
ejpam-6138	87	10	)	)	PUNCT
ejpam-6138	87	11	therefore	therefore	ADV
ejpam-6138	87	12	∫	∫	PROPN
ejpam-6138	87	13	ϑ	ϑ	X
ejpam-6138	87	14	θ	θ	PROPN
ejpam-6138	87	15	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	87	16	,	,	PUNCT
ejpam-6138	87	17	r)∣dr	r)∣dr	PROPN
ejpam-6138	87	18	=	=	SYM
ejpam-6138	87	19	ϱ	ϱ	ADP
ejpam-6138	87	20	1−σ	1−σ	NUM
ejpam-6138	87	21	γ(σ	γ(σ	PROPN
ejpam-6138	87	22	)	)	PUNCT
ejpam-6138	88	1	[	[	X
ejpam-6138	88	2	∫	∫	X
ejpam-6138	88	3	τ	τ	X
ejpam-6138	88	4	θ	θ	PROPN
ejpam-6138	88	5	(	(	PUNCT
ejpam-6138	88	6	(	(	PUNCT
ejpam-6138	88	7	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	88	8	)	)	PUNCT
ejpam-6138	88	9	(	(	PUNCT
ejpam-6138	88	10	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-6138	88	11	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-6138	88	12	−	−	NOUN
ejpam-6138	88	13	r	r	NOUN
ejpam-6138	88	14	ϱ)σ−1	ϱ)σ−1	NOUN
ejpam-6138	88	15	−	−	PROPN
ejpam-6138	88	16	r	r	NOUN
ejpam-6138	89	1	ϱ−1(τϱ	ϱ−1(τϱ	PROPN
ejpam-6138	89	2	−	−	NOUN
ejpam-6138	89	3	r	r	NOUN
ejpam-6138	89	4	ϱ)σ−1	ϱ)σ−1	NOUN
ejpam-6138	89	5	)	)	PUNCT
ejpam-6138	89	6	dr	dr	PROPN
ejpam-6138	89	7	+	+	PROPN
ejpam-6138	89	8	∫	∫	PROPN
ejpam-6138	89	9	ϑ	ϑ	X
ejpam-6138	89	10	τ	τ	X
ejpam-6138	89	11	(	(	PUNCT
ejpam-6138	89	12	(	(	PUNCT
ejpam-6138	89	13	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	89	14	)	)	PUNCT
ejpam-6138	89	15	(	(	PUNCT
ejpam-6138	89	16	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-6138	89	17	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-6138	89	18	−	−	NOUN
ejpam-6138	89	19	r	r	NOUN
ejpam-6138	89	20	ϱ)σ−1	ϱ)σ−1	NOUN
ejpam-6138	89	21	)	)	PUNCT
ejpam-6138	89	22	dr	dr	PROPN
ejpam-6138	89	23	]	]	PUNCT
ejpam-6138	89	24	.	.	PUNCT
ejpam-6138	90	1	we	we	PRON
ejpam-6138	90	2	calculate	calculate	VERB
ejpam-6138	90	3	the	the	DET
ejpam-6138	90	4	primitives	primitive	NOUN
ejpam-6138	90	5	by	by	ADP
ejpam-6138	90	6	integration	integration	NOUN
ejpam-6138	90	7	by	by	ADP
ejpam-6138	90	8	a	a	DET
ejpam-6138	90	9	change	change	NOUN
ejpam-6138	90	10	of	of	ADP
ejpam-6138	90	11	variable	variable	ADJ
ejpam-6138	90	12	∫	∫	PROPN
ejpam-6138	90	13	ϑ	ϑ	X
ejpam-6138	90	14	θ	θ	PROPN
ejpam-6138	90	15	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	90	16	,	,	PUNCT
ejpam-6138	90	17	r)∣dr	r)∣dr	PROPN
ejpam-6138	90	18	=	=	SYM
ejpam-6138	90	19	ϱ	ϱ	ADP
ejpam-6138	90	20	1−σ	1−σ	NUM
ejpam-6138	90	21	γ(σ	γ(σ	PROPN
ejpam-6138	90	22	)	)	PUNCT
ejpam-6138	90	23	[	[	PUNCT
ejpam-6138	90	24	(	(	PUNCT
ejpam-6138	90	25	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	90	26	)	)	PUNCT
ejpam-6138	90	27	(	(	PUNCT
ejpam-6138	90	28	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-6138	90	29	)	)	PUNCT
ejpam-6138	90	30	ϑ	ϑ	PROPN
ejpam-6138	90	31	ϱσ	ϱσ	X
ejpam-6138	90	32	ϱσ	ϱσ	PROPN
ejpam-6138	91	1	[	[	X
ejpam-6138	91	2	(	(	PUNCT
ejpam-6138	91	3	1	1	NUM
ejpam-6138	91	4	−	−	PROPN
ejpam-6138	91	5	θ	θ	SYM
ejpam-6138	91	6	ϱ	ϱ	ADP
ejpam-6138	91	7	ϑϱ	ϑϱ	PROPN
ejpam-6138	91	8	)	)	PUNCT
ejpam-6138	91	9	σ	σ	PROPN
ejpam-6138	91	10	−	−	PROPN
ejpam-6138	91	11	(	(	PUNCT
ejpam-6138	91	12	1	1	NUM
ejpam-6138	91	13	−	−	NOUN
ejpam-6138	91	14	τ	τ	X
ejpam-6138	91	15	ϱ	ϱ	ADP
ejpam-6138	91	16	ϑϱ	ϑϱ	INTJ
ejpam-6138	91	17	)	)	PUNCT
ejpam-6138	91	18	σ	σ	NOUN
ejpam-6138	91	19	]	]	PUNCT
ejpam-6138	91	20	−	−	X
ejpam-6138	91	21	τ	τ	PROPN
ejpam-6138	91	22	ϱσ	ϱσ	NOUN
ejpam-6138	91	23	ϱ	ϱ	PROPN
ejpam-6138	91	24	(	(	PUNCT
ejpam-6138	91	25	1	1	NUM
ejpam-6138	91	26	σ	σ	NOUN
ejpam-6138	91	27	(	(	PUNCT
ejpam-6138	91	28	1	1	NUM
ejpam-6138	91	29	−	−	PROPN
ejpam-6138	91	30	θ	θ	PROPN
ejpam-6138	91	31	ϱ	ϱ	ADP
ejpam-6138	91	32	τϱ	τϱ	X
ejpam-6138	91	33	)	)	PUNCT
ejpam-6138	91	34	σ	σ	PROPN
ejpam-6138	91	35	)	)	PUNCT
ejpam-6138	92	1	+	+	CCONJ
ejpam-6138	92	2	(	(	PUNCT
ejpam-6138	92	3	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	92	4	)	)	PUNCT
ejpam-6138	92	5	(	(	PUNCT
ejpam-6138	92	6	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-6138	92	7	)	)	PUNCT
ejpam-6138	92	8	ϑ	ϑ	PROPN
ejpam-6138	92	9	ϱσ	ϱσ	PROPN
ejpam-6138	92	10	ϱσ	ϱσ	PROPN
ejpam-6138	92	11	(	(	PUNCT
ejpam-6138	92	12	1	1	NUM
ejpam-6138	92	13	−	−	NOUN
ejpam-6138	92	14	τ	τ	X
ejpam-6138	92	15	ϱ	ϱ	ADP
ejpam-6138	92	16	ϑϱ	ϑϱ	INTJ
ejpam-6138	92	17	)	)	PUNCT
ejpam-6138	92	18	σ	σ	NOUN
ejpam-6138	92	19	]	]	PUNCT
ejpam-6138	92	20	=	=	PUNCT
ejpam-6138	92	21	ϱ	ϱ	ADP
ejpam-6138	92	22	1−σ	1−σ	NUM
ejpam-6138	92	23	γ(σ	γ(σ	PROPN
ejpam-6138	92	24	)	)	PUNCT
ejpam-6138	92	25	[	[	PUNCT
ejpam-6138	92	26	(	(	PUNCT
ejpam-6138	92	27	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	92	28	)	)	PUNCT
ejpam-6138	92	29	(	(	PUNCT
ejpam-6138	92	30	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-6138	92	31	)	)	PUNCT
ejpam-6138	92	32	ϑ	ϑ	PROPN
ejpam-6138	92	33	ϱσ	ϱσ	PROPN
ejpam-6138	92	34	ϱσ	ϱσ	PROPN
ejpam-6138	92	35	[	[	PUNCT
ejpam-6138	92	36	(	(	PUNCT
ejpam-6138	92	37	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-6138	92	38	ϑϱσ	ϑϱσ	INTJ
ejpam-6138	92	39	−	−	PROPN
ejpam-6138	93	1	(	(	PUNCT
ejpam-6138	93	2	ϑϱ−τϱ)σ	ϑϱ−τϱ)σ	PROPN
ejpam-6138	93	3	ϑϱσ	ϑϱσ	X
ejpam-6138	93	4	]	]	PUNCT
ejpam-6138	93	5	−	−	PROPN
ejpam-6138	94	1	τ	τ	X
ejpam-6138	94	2	ϱσ	ϱσ	NOUN
ejpam-6138	94	3	ϱ	ϱ	PROPN
ejpam-6138	94	4	(	(	PUNCT
ejpam-6138	94	5	1	1	NUM
ejpam-6138	94	6	σ	σ	NOUN
ejpam-6138	94	7	(	(	PUNCT
ejpam-6138	94	8	τϱ−θϱ)σ	τϱ−θϱ)σ	PROPN
ejpam-6138	94	9	τϱσ	τϱσ	NOUN
ejpam-6138	94	10	)	)	PUNCT
ejpam-6138	95	1	+	+	CCONJ
ejpam-6138	95	2	(	(	PUNCT
ejpam-6138	95	3	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	95	4	)	)	PUNCT
ejpam-6138	95	5	(	(	PUNCT
ejpam-6138	95	6	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-6138	95	7	)	)	PUNCT
ejpam-6138	95	8	ϑ	ϑ	PROPN
ejpam-6138	95	9	ϱσ	ϱσ	PROPN
ejpam-6138	95	10	ϱσ	ϱσ	PROPN
ejpam-6138	95	11	(	(	PUNCT
ejpam-6138	95	12	ϑϱ−τϱ)σ	ϑϱ−τϱ)σ	PROPN
ejpam-6138	95	13	ϑϱσ	ϑϱσ	X
ejpam-6138	95	14	]	]	PUNCT
ejpam-6138	95	15	=	=	PUNCT
ejpam-6138	95	16	ϱ	ϱ	ADP
ejpam-6138	95	17	1−σ	1−σ	NUM
ejpam-6138	95	18	ϱσγ(σ	ϱσγ(σ	PROPN
ejpam-6138	95	19	)	)	PUNCT
ejpam-6138	95	20	[	[	PUNCT
ejpam-6138	95	21	(	(	PUNCT
ejpam-6138	95	22	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-6138	95	23	)	)	PUNCT
ejpam-6138	95	24	(	(	PUNCT
ejpam-6138	95	25	ϑϱ−θϱ)(ϑ	ϑϱ−θϱ)(ϑ	ADJ
ejpam-6138	95	26	ϱ	ϱ	ADP
ejpam-6138	95	27	−	−	PROPN
ejpam-6138	95	28	θ	θ	PROPN
ejpam-6138	95	29	ϱ)σ	ϱ)σ	PUNCT
ejpam-6138	95	30	−	−	PROPN
ejpam-6138	95	31	(	(	PUNCT
ejpam-6138	95	32	τϱ	τϱ	ADP
ejpam-6138	95	33	−	−	PROPN
ejpam-6138	95	34	θ	θ	PROPN
ejpam-6138	95	35	ϱ)σ	ϱ)σ	X
ejpam-6138	95	36	]	]	PUNCT
ejpam-6138	95	37	.	.	PUNCT
ejpam-6138	96	1	then	then	ADV
ejpam-6138	96	2	,	,	PUNCT
ejpam-6138	96	3	∫	∫	PROPN
ejpam-6138	96	4	ϑ	ϑ	X
ejpam-6138	96	5	θ	θ	PROPN
ejpam-6138	96	6	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	96	7	,	,	PUNCT
ejpam-6138	96	8	r)∣	r)∣	PROPN
ejpam-6138	96	9	dr	dr	PROPN
ejpam-6138	96	10	=	=	PROPN
ejpam-6138	96	11	1	1	NUM
ejpam-6138	96	12	ϱσσγ(σ	ϱσσγ(σ	NOUN
ejpam-6138	96	13	)	)	PUNCT
ejpam-6138	97	1	[	[	X
ejpam-6138	97	2	(	(	PUNCT
ejpam-6138	97	3	ϑ	ϑ	X
ejpam-6138	97	4	ϱ	ϱ	ADP
ejpam-6138	97	5	−	−	PROPN
ejpam-6138	97	6	θ	θ	NOUN
ejpam-6138	97	7	ϱ)σ−1(τϱ	ϱ)σ−1(τϱ	NOUN
ejpam-6138	97	8	−	−	NUM
ejpam-6138	97	9	θ	θ	PROPN
ejpam-6138	97	10	ϱ	ϱ	NOUN
ejpam-6138	97	11	)	)	PUNCT
ejpam-6138	97	12	−	−	PROPN
ejpam-6138	97	13	(	(	PUNCT
ejpam-6138	97	14	τϱ	τϱ	ADP
ejpam-6138	97	15	−	−	PROPN
ejpam-6138	97	16	θ	θ	PROPN
ejpam-6138	97	17	ϱ)σ	ϱ)σ	NOUN
ejpam-6138	97	18	]	]	PUNCT
ejpam-6138	97	19	.	.	PUNCT
ejpam-6138	98	1	this	this	PRON
ejpam-6138	98	2	implies	imply	VERB
ejpam-6138	98	3	that	that	SCONJ
ejpam-6138	98	4	∫	∫	PROPN
ejpam-6138	98	5	ϑ	ϑ	X
ejpam-6138	98	6	θ	θ	PROPN
ejpam-6138	98	7	∂∣h̵(τ	∂∣h̵(τ	PROPN
ejpam-6138	98	8	,	,	PUNCT
ejpam-6138	98	9	r)∣	r)∣	PROPN
ejpam-6138	98	10	∂τ	∂τ	PROPN
ejpam-6138	98	11	dr	dr	PROPN
ejpam-6138	98	12	=	=	SYM
ejpam-6138	98	13	1	1	NUM
ejpam-6138	98	14	ϱσ−1σγ(σ	ϱσ−1σγ(σ	NOUN
ejpam-6138	98	15	)	)	PUNCT
ejpam-6138	99	1	[	[	X
ejpam-6138	99	2	(	(	PUNCT
ejpam-6138	99	3	ϑ	ϑ	X
ejpam-6138	99	4	ϱ	ϱ	ADP
ejpam-6138	99	5	−	−	PROPN
ejpam-6138	99	6	θ	θ	PROPN
ejpam-6138	99	7	ϱ)σ−1τϱ−1	ϱ)σ−1τϱ−1	NOUN
ejpam-6138	99	8	−	−	PROPN
ejpam-6138	100	1	σ(τϱ	σ(τϱ	DET
ejpam-6138	100	2	−	−	NOUN
ejpam-6138	100	3	θ	θ	NOUN
ejpam-6138	100	4	ϱ)σ−1τϱ−1	ϱ)σ−1τϱ−1	NOUN
ejpam-6138	100	5	]	]	PUNCT
ejpam-6138	100	6	,	,	PUNCT
ejpam-6138	100	7	(	(	PUNCT
ejpam-6138	100	8	3.6	3.6	NUM
ejpam-6138	100	9	)	)	PUNCT
ejpam-6138	100	10	which	which	PRON
ejpam-6138	100	11	ends	end	VERB
ejpam-6138	100	12	the	the	DET
ejpam-6138	100	13	proof	proof	NOUN
ejpam-6138	100	14	.	.	PUNCT
ejpam-6138	101	1	corollary	corollary	ADJ
ejpam-6138	101	2	1	1	NUM
ejpam-6138	101	3	.	.	PUNCT
ejpam-6138	102	1	we	we	PRON
ejpam-6138	102	2	can	can	AUX
ejpam-6138	102	3	define	define	VERB
ejpam-6138	102	4	the	the	DET
ejpam-6138	102	5	continuous	continuous	ADJ
ejpam-6138	102	6	functions	function	NOUN
ejpam-6138	102	7	ξ	ξ	PROPN
ejpam-6138	102	8	and	and	CCONJ
ejpam-6138	102	9	ξ	ξ	X
ejpam-6138	102	10	′	′	NUM
ejpam-6138	102	11	by	by	ADP
ejpam-6138	102	12	ξ(τ	ξ(τ	PROPN
ejpam-6138	102	13	)	)	PUNCT
ejpam-6138	102	14	=	=	PRON
ejpam-6138	103	1	(	(	PUNCT
ejpam-6138	103	2	ϑϱ	ϑϱ	ADP
ejpam-6138	103	3	−	−	NUM
ejpam-6138	103	4	θ	θ	NOUN
ejpam-6138	104	1	ϱ)σ−1(τϱ	ϱ)σ−1(τϱ	NOUN
ejpam-6138	104	2	−	−	NUM
ejpam-6138	104	3	θ	θ	PROPN
ejpam-6138	104	4	ϱ	ϱ	NOUN
ejpam-6138	104	5	)	)	PUNCT
ejpam-6138	104	6	−	−	PROPN
ejpam-6138	104	7	(	(	PUNCT
ejpam-6138	104	8	τϱ	τϱ	ADP
ejpam-6138	104	9	−	−	PROPN
ejpam-6138	104	10	θ	θ	PROPN
ejpam-6138	104	11	ϱ)σ	ϱ)σ	PROPN
ejpam-6138	104	12	,	,	PUNCT
ejpam-6138	104	13	τ	τ	PROPN
ejpam-6138	104	14	∈	∈	PROPN
ejpam-6138	105	1	[	[	X
ejpam-6138	105	2	θ	θ	X
ejpam-6138	105	3	,	,	PUNCT
ejpam-6138	105	4	ϑ	ϑ	X
ejpam-6138	105	5	]	]	X
ejpam-6138	105	6	,	,	PUNCT
ejpam-6138	105	7	(	(	PUNCT
ejpam-6138	105	8	3.7	3.7	NUM
ejpam-6138	105	9	)	)	PUNCT
ejpam-6138	105	10	and	and	CCONJ
ejpam-6138	105	11	ξ	ξ	NOUN
ejpam-6138	105	12	′(τ	′(τ	NOUN
ejpam-6138	105	13	)	)	PUNCT
ejpam-6138	105	14	=	=	PUNCT
ejpam-6138	106	1	(	(	PUNCT
ejpam-6138	106	2	ϑϱ	ϑϱ	ADP
ejpam-6138	106	3	−	−	PROPN
ejpam-6138	106	4	θ	θ	PROPN
ejpam-6138	106	5	ϱ)σ−1τϱ−1	ϱ)σ−1τϱ−1	NOUN
ejpam-6138	106	6	−	−	PROPN
ejpam-6138	107	1	σ(τϱ	σ(τϱ	DET
ejpam-6138	107	2	−	−	NOUN
ejpam-6138	107	3	θ	θ	NOUN
ejpam-6138	107	4	ϱ)σ−1τϱ−1	ϱ)σ−1τϱ−1	PROPN
ejpam-6138	107	5	,	,	PUNCT
ejpam-6138	107	6	τ	τ	PROPN
ejpam-6138	107	7	∈	∈	PROPN
ejpam-6138	108	1	[	[	X
ejpam-6138	108	2	θ	θ	X
ejpam-6138	108	3	,	,	PUNCT
ejpam-6138	108	4	ϑ	ϑ	X
ejpam-6138	108	5	]	]	X
ejpam-6138	108	6	.	.	PUNCT
ejpam-6138	109	1	(	(	PUNCT
ejpam-6138	109	2	3.8	3.8	NUM
ejpam-6138	109	3	)	)	PUNCT
ejpam-6138	109	4	z.	z.	PROPN
ejpam-6138	109	5	bekri	bekri	PROPN
ejpam-6138	109	6	et	et	PROPN
ejpam-6138	109	7	al	al	PROPN
ejpam-6138	109	8	.	.	PUNCT
ejpam-6138	109	9	/	/	SYM
ejpam-6138	109	10	eur	eur	PROPN
ejpam-6138	109	11	.	.	PUNCT
ejpam-6138	110	1	j.	j.	PROPN
ejpam-6138	110	2	pure	pure	PROPN
ejpam-6138	110	3	appl	appl	PROPN
ejpam-6138	110	4	.	.	PROPN
ejpam-6138	110	5	math	math	PROPN
ejpam-6138	110	6	,	,	PUNCT
ejpam-6138	110	7	18	18	NUM
ejpam-6138	110	8	(	(	PUNCT
ejpam-6138	110	9	2	2	NUM
ejpam-6138	110	10	)	)	PUNCT
ejpam-6138	110	11	(	(	PUNCT
ejpam-6138	110	12	2025	2025	NUM
ejpam-6138	110	13	)	)	PUNCT
ejpam-6138	110	14	,	,	PUNCT
ejpam-6138	110	15	6138	6138	NUM
ejpam-6138	110	16	6	6	NUM
ejpam-6138	110	17	of	of	ADP
ejpam-6138	110	18	17	17	NUM
ejpam-6138	110	19	proposition	proposition	NOUN
ejpam-6138	110	20	2	2	NUM
ejpam-6138	110	21	.	.	PUNCT
ejpam-6138	111	1	by	by	ADP
ejpam-6138	111	2	(	(	PUNCT
ejpam-6138	111	3	3.3	3.3	NUM
ejpam-6138	111	4	)	)	PUNCT
ejpam-6138	111	5	and	and	CCONJ
ejpam-6138	111	6	(	(	PUNCT
ejpam-6138	111	7	3.4	3.4	NUM
ejpam-6138	111	8	)	)	PUNCT
ejpam-6138	111	9	,	,	PUNCT
ejpam-6138	111	10	suppose	suppose	VERB
ejpam-6138	111	11	that	that	SCONJ
ejpam-6138	111	12	θ	θ	PROPN
ejpam-6138	111	13	=	=	SYM
ejpam-6138	111	14	0	0	NUM
ejpam-6138	111	15	,	,	PUNCT
ejpam-6138	111	16	θ	θ	X
ejpam-6138	111	17	<	<	X
ejpam-6138	111	18	ϑ	ϑ	X
ejpam-6138	111	19	then	then	ADV
ejpam-6138	111	20	∫	∫	PROPN
ejpam-6138	111	21	ϑ	ϑ	X
ejpam-6138	111	22	0	0	NUM
ejpam-6138	111	23	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	111	24	,	,	PUNCT
ejpam-6138	111	25	r)∣dr	r)∣dr	X
ejpam-6138	111	26	≤	≤	ADV
ejpam-6138	111	27	1	1	NUM
ejpam-6138	111	28	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	111	29	)	)	PUNCT
ejpam-6138	111	30	[	[	PUNCT
ejpam-6138	111	31	ϑ	ϑ	PROPN
ejpam-6138	111	32	ϱσ	ϱσ	PROPN
ejpam-6138	111	33	σ	σ	PROPN
ejpam-6138	111	34	1	1	PROPN
ejpam-6138	111	35	/	/	SYM
ejpam-6138	112	1	σ−1	σ−1	PROPN
ejpam-6138	112	2	−	−	NOUN
ejpam-6138	112	3	ϑ	ϑ	PROPN
ejpam-6138	112	4	ϱσ	ϱσ	PROPN
ejpam-6138	112	5	σ	σ	PROPN
ejpam-6138	112	6	σ	σ	PROPN
ejpam-6138	112	7	/	/	SYM
ejpam-6138	112	8	σ−1	σ−1	PROPN
ejpam-6138	112	9	]	]	PUNCT
ejpam-6138	112	10	,	,	PUNCT
ejpam-6138	112	11	(	(	PUNCT
ejpam-6138	112	12	3.9	3.9	NUM
ejpam-6138	112	13	)	)	PUNCT
ejpam-6138	112	14	and	and	CCONJ
ejpam-6138	112	15	∫	∫	PROPN
ejpam-6138	112	16	ϑ	ϑ	X
ejpam-6138	112	17	0	0	NUM
ejpam-6138	112	18	∂∣h̵(τ	∂∣h̵(τ	PROPN
ejpam-6138	112	19	,	,	PUNCT
ejpam-6138	112	20	r)∣	r)∣	PROPN
ejpam-6138	112	21	∂τ	∂τ	PROPN
ejpam-6138	112	22	dr	dr	PROPN
ejpam-6138	112	23	≤	≤	PROPN
ejpam-6138	112	24	1	1	NUM
ejpam-6138	112	25	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	NOUN
ejpam-6138	112	26	)	)	PUNCT
ejpam-6138	113	1	[	[	X
ejpam-6138	113	2	ϑ	ϑ	X
ejpam-6138	113	3	(	(	PUNCT
ejpam-6138	113	4	ϱσ−1	ϱσ−1	PROPN
ejpam-6138	113	5	)	)	PUNCT
ejpam-6138	113	6	(	(	PUNCT
ejpam-6138	113	7	ϱ−1	ϱ−1	PROPN
ejpam-6138	113	8	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	113	9	)	)	PUNCT
ejpam-6138	113	10	)	)	PUNCT
ejpam-6138	113	11	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	113	12	)	)	PUNCT
ejpam-6138	113	13	−	−	PROPN
ejpam-6138	113	14	σ(ϑ)ϱσ−1	σ(ϑ)ϱσ−1	PROPN
ejpam-6138	113	15	(	(	PUNCT
ejpam-6138	113	16	ϱ−1	ϱ−1	PROPN
ejpam-6138	113	17	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	113	18	)	)	PUNCT
ejpam-6138	113	19	)	)	PUNCT
ejpam-6138	113	20	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	113	21	)	)	PUNCT
ejpam-6138	113	22	]	]	PUNCT
ejpam-6138	113	23	.	.	PUNCT
ejpam-6138	114	1	(	(	PUNCT
ejpam-6138	114	2	3.10	3.10	NUM
ejpam-6138	114	3	)	)	PUNCT
ejpam-6138	114	4	proof	proof	NOUN
ejpam-6138	114	5	.	.	PUNCT
ejpam-6138	115	1	according	accord	VERB
ejpam-6138	115	2	by	by	ADP
ejpam-6138	115	3	corollary	corollary	ADJ
ejpam-6138	115	4	1	1	NUM
ejpam-6138	115	5	,	,	PUNCT
ejpam-6138	115	6	differentiating	differentiate	VERB
ejpam-6138	115	7	the	the	DET
ejpam-6138	115	8	functions	function	NOUN
ejpam-6138	115	9	ξ	ξ	PROPN
ejpam-6138	115	10	,	,	PUNCT
ejpam-6138	115	11	ξ	ξ	NOUN
ejpam-6138	115	12	′	′	NUM
ejpam-6138	115	13	and	and	CCONJ
ejpam-6138	115	14	directly	directly	ADV
ejpam-6138	115	15	deduce	deduce	VERB
ejpam-6138	115	16	that	that	SCONJ
ejpam-6138	115	17	the	the	DET
ejpam-6138	115	18	maximum	maximum	NOUN
ejpam-6138	115	19	was	be	AUX
ejpam-6138	115	20	reached	reach	VERB
ejpam-6138	115	21	at	at	ADP
ejpam-6138	115	22	the	the	DET
ejpam-6138	115	23	points	point	NOUN
ejpam-6138	115	24	τ	τ	PROPN
ejpam-6138	115	25	∗	∗	NOUN
ejpam-6138	115	26	=	=	SYM
ejpam-6138	115	27	ϑ	ϑ	PROPN
ejpam-6138	115	28	σ	σ	NOUN
ejpam-6138	115	29	1/ϱ(σ−1	1/ϱ(σ−1	NUM
ejpam-6138	115	30	)	)	PUNCT
ejpam-6138	115	31	,	,	PUNCT
ejpam-6138	115	32	τ	τ	PROPN
ejpam-6138	115	33	∗	∗	NOUN
ejpam-6138	115	34	1	1	NUM
ejpam-6138	115	35	=	=	SYM
ejpam-6138	115	36	ϑ	ϑ	X
ejpam-6138	115	37	(	(	PUNCT
ejpam-6138	115	38	ϱ−1	ϱ−1	PROPN
ejpam-6138	115	39	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	115	40	)	)	PUNCT
ejpam-6138	115	41	)	)	PUNCT
ejpam-6138	115	42	1/ϱ(σ−1	1/ϱ(σ−1	NUM
ejpam-6138	115	43	)	)	PUNCT
ejpam-6138	115	44	.	.	PUNCT
ejpam-6138	116	1	moreover	moreover	ADV
ejpam-6138	116	2	,	,	PUNCT
ejpam-6138	116	3	ξ(τ∗	ξ(τ∗	ADP
ejpam-6138	116	4	)	)	PUNCT
ejpam-6138	116	5	=	=	SYM
ejpam-6138	116	6	1	1	NUM
ejpam-6138	116	7	ϱσ	ϱσ	NOUN
ejpam-6138	116	8	(	(	PUNCT
ejpam-6138	116	9	ϑ	ϑ	X
ejpam-6138	116	10	ϱσ	ϱσ	PROPN
ejpam-6138	116	11	σ	σ	PROPN
ejpam-6138	116	12	1	1	PROPN
ejpam-6138	116	13	/	/	SYM
ejpam-6138	117	1	σ−1	σ−1	PROPN
ejpam-6138	117	2	−	−	NOUN
ejpam-6138	117	3	ϑ	ϑ	PROPN
ejpam-6138	117	4	ϱσ	ϱσ	PROPN
ejpam-6138	117	5	σ	σ	PROPN
ejpam-6138	117	6	σ	σ	PROPN
ejpam-6138	117	7	/	/	SYM
ejpam-6138	117	8	σ−1	σ−1	PROPN
ejpam-6138	117	9	)	)	PUNCT
ejpam-6138	117	10	,	,	PUNCT
ejpam-6138	117	11	ξ	ξ	X
ejpam-6138	117	12	′(τ∗1	′(τ∗1	PUNCT
ejpam-6138	117	13	)	)	PUNCT
ejpam-6138	117	14	=	=	SYM
ejpam-6138	118	1	1	1	NUM
ejpam-6138	118	2	ϱσ−1	ϱσ−1	PROPN
ejpam-6138	118	3	(	(	PUNCT
ejpam-6138	118	4	ϑϱσ−1	ϑϱσ−1	PROPN
ejpam-6138	118	5	(	(	PUNCT
ejpam-6138	118	6	ϱ−1	ϱ−1	PROPN
ejpam-6138	118	7	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	118	8	)	)	PUNCT
ejpam-6138	118	9	)	)	PUNCT
ejpam-6138	118	10	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	118	11	)	)	PUNCT
ejpam-6138	118	12	−	−	PROPN
ejpam-6138	119	1	σ(ϑ)ϱσ−1	σ(ϑ)ϱσ−1	PROPN
ejpam-6138	119	2	(	(	PUNCT
ejpam-6138	119	3	ϱ−1	ϱ−1	PROPN
ejpam-6138	119	4	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	119	5	)	)	PUNCT
ejpam-6138	119	6	)	)	PUNCT
ejpam-6138	119	7	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	119	8	)	)	PUNCT
ejpam-6138	119	9	)	)	PUNCT
ejpam-6138	119	10	,	,	PUNCT
ejpam-6138	119	11	that	that	PRON
ejpam-6138	119	12	finishes	finish	VERB
ejpam-6138	119	13	the	the	DET
ejpam-6138	119	14	proof	proof	NOUN
ejpam-6138	119	15	.	.	PUNCT
ejpam-6138	120	1	theorem	theorem	NOUN
ejpam-6138	120	2	2	2	NUM
ejpam-6138	120	3	.	.	PUNCT
ejpam-6138	120	4	assume	assume	VERB
ejpam-6138	120	5	ξ	ξ	X
ejpam-6138	121	1	∶	∶	NOUN
ejpam-6138	121	2	[	[	X
ejpam-6138	121	3	0	0	NUM
ejpam-6138	121	4	,	,	PUNCT
ejpam-6138	121	5	ϑ	ϑ	X
ejpam-6138	121	6	]	]	X
ejpam-6138	121	7	×	×	NOUN
ejpam-6138	121	8	r2	r2	PROPN
ejpam-6138	121	9	⟶	⟶	NOUN
ejpam-6138	121	10	r	r	NOUN
ejpam-6138	121	11	is	be	AUX
ejpam-6138	121	12	a	a	DET
ejpam-6138	121	13	function	function	NOUN
ejpam-6138	121	14	is	be	AUX
ejpam-6138	121	15	continuous	continuous	ADJ
ejpam-6138	121	16	and	and	CCONJ
ejpam-6138	121	17	check	check	VERB
ejpam-6138	121	18	a	a	DET
ejpam-6138	121	19	condition	condition	NOUN
ejpam-6138	121	20	of	of	ADP
ejpam-6138	121	21	uniform	uniform	ADJ
ejpam-6138	121	22	lipschitz	lipschitz	NOUN
ejpam-6138	121	23	concerning	concern	VERB
ejpam-6138	121	24	the	the	DET
ejpam-6138	121	25	second	second	ADJ
ejpam-6138	121	26	variable	variable	NOUN
ejpam-6138	121	27	on	on	ADP
ejpam-6138	121	28	[	[	X
ejpam-6138	121	29	0	0	NUM
ejpam-6138	121	30	,	,	PUNCT
ejpam-6138	121	31	ϑ]×r2	ϑ]×r2	PROPN
ejpam-6138	121	32	with	with	ADP
ejpam-6138	121	33	lipschitz	lipschitz	VERB
ejpam-6138	121	34	real	real	ADJ
ejpam-6138	121	35	ζ	ζ	NOUN
ejpam-6138	121	36	,	,	PUNCT
ejpam-6138	121	37	thus	thus	ADV
ejpam-6138	121	38	,	,	PUNCT
ejpam-6138	121	39	»	»	PUNCT
ejpam-6138	121	40	»	»	PUNCT
ejpam-6138	121	41	»	»	PUNCT
ejpam-6138	121	42	»	»	PUNCT
ejpam-6138	121	43	»	»	PUNCT
ejpam-6138	121	44	»	»	X
ejpam-6138	121	45	ξ	ξ	X
ejpam-6138	121	46	(	(	PUNCT
ejpam-6138	121	47	τ	τ	PROPN
ejpam-6138	121	48	,	,	PUNCT
ejpam-6138	121	49	µ	µ	NOUN
ejpam-6138	121	50	,	,	PUNCT
ejpam-6138	121	51	µ′	µ′	NUM
ejpam-6138	121	52	)	)	PUNCT
ejpam-6138	122	1	−	−	PROPN
ejpam-6138	122	2	ξ(τ	ξ(τ	PROPN
ejpam-6138	122	3	,	,	PUNCT
ejpam-6138	122	4	ν	ν	NOUN
ejpam-6138	122	5	,	,	PUNCT
ejpam-6138	122	6	ν	ν	NOUN
ejpam-6138	122	7	′	′	NUM
ejpam-6138	122	8	)	)	PUNCT
ejpam-6138	122	9	»	»	NOUN
ejpam-6138	122	10	»	»	PUNCT
ejpam-6138	122	11	»	»	PUNCT
ejpam-6138	122	12	»	»	PRON
ejpam-6138	122	13	»	»	ADV
ejpam-6138	122	14	»	»	X
ejpam-6138	122	15	≤	≤	X
ejpam-6138	122	16	ζ∣µ	ζ∣µ	PUNCT
ejpam-6138	122	17	−	−	PROPN
ejpam-6138	122	18	ν∣	ν∣	NOUN
ejpam-6138	122	19	+	+	PUNCT
ejpam-6138	122	20	η∣µ′	η∣µ′	NOUN
ejpam-6138	122	21	−	−	NOUN
ejpam-6138	122	22	ν	ν	NOUN
ejpam-6138	122	23	′∣	′∣	PROPN
ejpam-6138	122	24	,	,	PUNCT
ejpam-6138	122	25	(	(	PUNCT
ejpam-6138	122	26	3.11	3.11	NUM
ejpam-6138	122	27	)	)	PUNCT
ejpam-6138	122	28	for	for	ADP
ejpam-6138	122	29	(	(	PUNCT
ejpam-6138	122	30	τ	τ	PROPN
ejpam-6138	122	31	,	,	PUNCT
ejpam-6138	122	32	µ	µ	NOUN
ejpam-6138	122	33	,	,	PUNCT
ejpam-6138	122	34	µ′	µ′	NOUN
ejpam-6138	122	35	)	)	PUNCT
ejpam-6138	122	36	,	,	PUNCT
ejpam-6138	122	37	(	(	PUNCT
ejpam-6138	122	38	τ	τ	X
ejpam-6138	122	39	,	,	PUNCT
ejpam-6138	122	40	ν	ν	PROPN
ejpam-6138	122	41	,	,	PUNCT
ejpam-6138	122	42	ν	ν	NOUN
ejpam-6138	122	43	′	′	NOUN
ejpam-6138	122	44	)	)	PUNCT
ejpam-6138	122	45	∈	∈	PROPN
ejpam-6138	123	1	[	[	X
ejpam-6138	123	2	0	0	NUM
ejpam-6138	123	3	,	,	PUNCT
ejpam-6138	123	4	ϑ	ϑ	X
ejpam-6138	123	5	]	]	X
ejpam-6138	123	6	×	×	NOUN
ejpam-6138	123	7	r2	r2	NOUN
ejpam-6138	123	8	,	,	PUNCT
ejpam-6138	123	9	where	where	SCONJ
ejpam-6138	123	10	η	η	PROPN
ejpam-6138	123	11	≥	≥	X
ejpam-6138	123	12	0	0	NUM
ejpam-6138	123	13	,	,	PUNCT
ejpam-6138	123	14	ζ	ζ	NOUN
ejpam-6138	123	15	>	>	SYM
ejpam-6138	123	16	0	0	NUM
ejpam-6138	123	17	are	be	AUX
ejpam-6138	123	18	constants	constant	NOUN
ejpam-6138	123	19	.	.	PUNCT
ejpam-6138	124	1	if	if	SCONJ
ejpam-6138	124	2	ζ	ζ	NOUN
ejpam-6138	124	3	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	124	4	)	)	PUNCT
ejpam-6138	124	5	[	[	PUNCT
ejpam-6138	124	6	ϑ	ϑ	PROPN
ejpam-6138	124	7	ϱσ	ϱσ	PROPN
ejpam-6138	124	8	σ	σ	PROPN
ejpam-6138	124	9	1	1	PROPN
ejpam-6138	124	10	/	/	SYM
ejpam-6138	125	1	σ−1	σ−1	PROPN
ejpam-6138	125	2	−	−	NOUN
ejpam-6138	125	3	ϑ	ϑ	PROPN
ejpam-6138	125	4	ϱσ	ϱσ	PROPN
ejpam-6138	125	5	σ	σ	PROPN
ejpam-6138	125	6	σ	σ	PROPN
ejpam-6138	125	7	/	/	SYM
ejpam-6138	125	8	σ−1	σ−1	PROPN
ejpam-6138	125	9	]	]	PUNCT
ejpam-6138	126	1	+	+	CCONJ
ejpam-6138	126	2	η	η	PROPN
ejpam-6138	126	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	126	4	)	)	PUNCT
ejpam-6138	127	1	[	[	X
ejpam-6138	127	2	ϑ	ϑ	X
ejpam-6138	127	3	ϱσ−1	ϱσ−1	PROPN
ejpam-6138	127	4	(	(	PUNCT
ejpam-6138	127	5	ϱ−1	ϱ−1	PROPN
ejpam-6138	127	6	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	127	7	)	)	PUNCT
ejpam-6138	127	8	)	)	PUNCT
ejpam-6138	127	9	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	127	10	)	)	PUNCT
ejpam-6138	127	11	−σ(ϑ)ϱσ−1	−σ(ϑ)ϱσ−1	NOUN
ejpam-6138	127	12	(	(	PUNCT
ejpam-6138	127	13	ϱ−1	ϱ−1	PROPN
ejpam-6138	127	14	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	127	15	)	)	PUNCT
ejpam-6138	127	16	)	)	PUNCT
ejpam-6138	127	17	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	127	18	)	)	PUNCT
ejpam-6138	127	19	]	]	PUNCT
ejpam-6138	127	20	<	<	X
ejpam-6138	127	21	1	1	X
ejpam-6138	127	22	.	.	PUNCT
ejpam-6138	127	23	(	(	PUNCT
ejpam-6138	127	24	3.12	3.12	NUM
ejpam-6138	127	25	)	)	PUNCT
ejpam-6138	127	26	then	then	ADV
ejpam-6138	127	27	the	the	DET
ejpam-6138	127	28	bvp	bvp	PROPN
ejpam-6138	127	29	{	{	PUNCT
ejpam-6138	127	30	ϱ	ϱ	PROPN
ejpam-6138	127	31	cd	cd	PROPN
ejpam-6138	127	32	σ	σ	PROPN
ejpam-6138	127	33	0+µ(τ	0+µ(τ	PROPN
ejpam-6138	127	34	)	)	PUNCT
ejpam-6138	127	35	=	=	SYM
ejpam-6138	127	36	−ξ	−ξ	NOUN
ejpam-6138	127	37	(	(	PUNCT
ejpam-6138	127	38	τ	τ	PROPN
ejpam-6138	127	39	,	,	PUNCT
ejpam-6138	127	40	µ(τ	µ(τ	PROPN
ejpam-6138	127	41	)	)	PUNCT
ejpam-6138	127	42	,	,	PUNCT
ejpam-6138	127	43	ϱcdς	ϱcdς	ADJ
ejpam-6138	127	44	0+µ(τ	0+µ(τ	NOUN
ejpam-6138	127	45	)	)	PUNCT
ejpam-6138	127	46	)	)	PUNCT
ejpam-6138	127	47	,	,	PUNCT
ejpam-6138	127	48	0	0	PUNCT
ejpam-6138	127	49	<	<	X
ejpam-6138	127	50	τ	τ	X
ejpam-6138	127	51	<	<	X
ejpam-6138	127	52	ϑ	ϑ	X
ejpam-6138	127	53	,	,	PUNCT
ejpam-6138	127	54	µ(0	µ(0	NOUN
ejpam-6138	127	55	)	)	PUNCT
ejpam-6138	127	56	=	=	SYM
ejpam-6138	127	57	λ1	λ1	ADJ
ejpam-6138	127	58	,	,	PUNCT
ejpam-6138	127	59	µ(ϑ	µ(ϑ	PROPN
ejpam-6138	127	60	)	)	PUNCT
ejpam-6138	127	61	=	=	SYM
ejpam-6138	127	62	λ2	λ2	NOUN
ejpam-6138	127	63	,	,	PUNCT
ejpam-6138	127	64	(	(	PUNCT
ejpam-6138	127	65	3.13	3.13	NUM
ejpam-6138	127	66	)	)	PUNCT
ejpam-6138	127	67	admits	admit	VERB
ejpam-6138	127	68	a	a	DET
ejpam-6138	127	69	single	single	ADJ
ejpam-6138	127	70	solution	solution	NOUN
ejpam-6138	127	71	.	.	PUNCT
ejpam-6138	128	1	z.	z.	PROPN
ejpam-6138	128	2	bekri	bekri	PROPN
ejpam-6138	128	3	et	et	PROPN
ejpam-6138	128	4	al	al	PROPN
ejpam-6138	128	5	.	.	PUNCT
ejpam-6138	128	6	/	/	SYM
ejpam-6138	128	7	eur	eur	PROPN
ejpam-6138	128	8	.	.	PUNCT
ejpam-6138	129	1	j.	j.	PROPN
ejpam-6138	129	2	pure	pure	PROPN
ejpam-6138	129	3	appl	appl	PROPN
ejpam-6138	129	4	.	.	PROPN
ejpam-6138	129	5	math	math	PROPN
ejpam-6138	129	6	,	,	PUNCT
ejpam-6138	129	7	18	18	NUM
ejpam-6138	129	8	(	(	PUNCT
ejpam-6138	129	9	2	2	NUM
ejpam-6138	129	10	)	)	PUNCT
ejpam-6138	129	11	(	(	PUNCT
ejpam-6138	129	12	2025	2025	NUM
ejpam-6138	129	13	)	)	PUNCT
ejpam-6138	129	14	,	,	PUNCT
ejpam-6138	129	15	6138	6138	NUM
ejpam-6138	129	16	7	7	NUM
ejpam-6138	129	17	of	of	ADP
ejpam-6138	129	18	17	17	NUM
ejpam-6138	129	19	proof	proof	NOUN
ejpam-6138	129	20	.	.	PUNCT
ejpam-6138	130	1	suppose	suppose	VERB
ejpam-6138	130	2	π	π	NOUN
ejpam-6138	130	3	is	be	AUX
ejpam-6138	130	4	a	a	DET
ejpam-6138	130	5	space	space	NOUN
ejpam-6138	130	6	of	of	ADP
ejpam-6138	130	7	banach	banach	ADV
ejpam-6138	130	8	fitted	fit	VERB
ejpam-6138	130	9	with	with	ADP
ejpam-6138	130	10	continuous	continuous	ADJ
ejpam-6138	130	11	applications	application	NOUN
ejpam-6138	130	12	defined	define	VERB
ejpam-6138	130	13	on	on	ADP
ejpam-6138	130	14	[	[	X
ejpam-6138	130	15	0	0	NUM
ejpam-6138	130	16	,	,	PUNCT
ejpam-6138	130	17	ϑ	ϑ	X
ejpam-6138	130	18	]	]	X
ejpam-6138	130	19	with	with	ADP
ejpam-6138	130	20	the	the	DET
ejpam-6138	130	21	norm	norm	NOUN
ejpam-6138	130	22	∥µ∥	∥µ∥	NOUN
ejpam-6138	130	23	=	=	SYM
ejpam-6138	130	24	max	max	PROPN
ejpam-6138	131	1	τ∈[0,ϑ	τ∈[0,ϑ	PROPN
ejpam-6138	131	2	]	]	X
ejpam-6138	131	3	{	{	PUNCT
ejpam-6138	131	4	ζ∣µ(τ)∣	ζ∣µ(τ)∣	PROPN
ejpam-6138	131	5	+	+	NOUN
ejpam-6138	131	6	η∣µ′(τ)∣	η∣µ′(τ)∣	NUM
ejpam-6138	131	7	}	}	PUNCT
ejpam-6138	131	8	.	.	PUNCT
ejpam-6138	132	1	according	accord	VERB
ejpam-6138	132	2	to	to	ADP
ejpam-6138	132	3	lemma	lemma	PROPN
ejpam-6138	132	4	2	2	NUM
ejpam-6138	132	5	,	,	PUNCT
ejpam-6138	132	6	we	we	PRON
ejpam-6138	132	7	have	have	VERB
ejpam-6138	132	8	µ	µ	PRON
ejpam-6138	132	9	∈	∈	PROPN
ejpam-6138	132	10	c[0	c[0	PROPN
ejpam-6138	132	11	,	,	PUNCT
ejpam-6138	132	12	ϑ	ϑ	X
ejpam-6138	132	13	]	]	X
ejpam-6138	132	14	is	be	AUX
ejpam-6138	132	15	a	a	DET
ejpam-6138	132	16	solution	solution	NOUN
ejpam-6138	132	17	of	of	ADP
ejpam-6138	132	18	(	(	PUNCT
ejpam-6138	132	19	3.13	3.13	NUM
ejpam-6138	132	20	)	)	PUNCT
ejpam-6138	132	21	equivalent	equivalent	NOUN
ejpam-6138	132	22	that	that	SCONJ
ejpam-6138	132	23	this	this	PRON
ejpam-6138	132	24	is	be	AUX
ejpam-6138	132	25	the	the	DET
ejpam-6138	132	26	same	same	ADJ
ejpam-6138	132	27	as	as	ADP
ejpam-6138	132	28	the	the	DET
ejpam-6138	132	29	solving	solve	VERB
ejpam-6138	132	30	an	an	DET
ejpam-6138	132	31	equation	equation	NOUN
ejpam-6138	132	32	in	in	ADP
ejpam-6138	132	33	integral	integral	ADJ
ejpam-6138	132	34	form	form	NOUN
ejpam-6138	132	35	µ(τ	µ(τ	NOUN
ejpam-6138	132	36	)	)	PUNCT
ejpam-6138	132	37	=	=	PUNCT
ejpam-6138	133	1	[	[	X
ejpam-6138	133	2	(	(	PUNCT
ejpam-6138	133	3	λ2	λ2	NOUN
ejpam-6138	133	4	−	−	PROPN
ejpam-6138	133	5	λ1	λ1	PROPN
ejpam-6138	133	6	)	)	PUNCT
ejpam-6138	133	7	(	(	PUNCT
ejpam-6138	133	8	τ	τ	X
ejpam-6138	133	9	ϑ	ϑ	X
ejpam-6138	133	10	)	)	PUNCT
ejpam-6138	133	11	ϱ	ϱ	PROPN
ejpam-6138	133	12	+	+	X
ejpam-6138	133	13	λ1	λ1	ADJ
ejpam-6138	133	14	]	]	X
ejpam-6138	134	1	+	+	NUM
ejpam-6138	134	2	∫	∫	PROPN
ejpam-6138	134	3	ϑ	ϑ	X
ejpam-6138	134	4	0	0	NUM
ejpam-6138	134	5	h̵(τ	h̵(τ	PROPN
ejpam-6138	134	6	,	,	PUNCT
ejpam-6138	134	7	r	r	NOUN
ejpam-6138	134	8	)	)	PUNCT
ejpam-6138	134	9	ξ	ξ	PROPN
ejpam-6138	134	10	(	(	PUNCT
ejpam-6138	134	11	r	r	NOUN
ejpam-6138	134	12	,	,	PUNCT
ejpam-6138	134	13	µ(r	µ(r	NOUN
ejpam-6138	134	14	)	)	PUNCT
ejpam-6138	134	15	,	,	PUNCT
ejpam-6138	134	16	ϱcdς	ϱcdς	ADJ
ejpam-6138	134	17	0+µ(r	0+µ(r	NOUN
ejpam-6138	134	18	)	)	PUNCT
ejpam-6138	134	19	)	)	PUNCT
ejpam-6138	135	1	dr	dr	PROPN
ejpam-6138	135	2	.	.	PROPN
ejpam-6138	135	3	(	(	PUNCT
ejpam-6138	135	4	3.14	3.14	NUM
ejpam-6138	135	5	)	)	PUNCT
ejpam-6138	135	6	define	define	VERB
ejpam-6138	135	7	the	the	DET
ejpam-6138	135	8	operator	operator	NOUN
ejpam-6138	135	9	σ	σ	PROPN
ejpam-6138	135	10	∶	∶	NOUN
ejpam-6138	135	11	π	π	X
ejpam-6138	135	12	→	→	SYM
ejpam-6138	135	13	π	π	PROPN
ejpam-6138	135	14	by	by	ADP
ejpam-6138	135	15	σµ(τ	σµ(τ	NOUN
ejpam-6138	135	16	)	)	PUNCT
ejpam-6138	135	17	=	=	NOUN
ejpam-6138	136	1	[	[	X
ejpam-6138	136	2	(	(	PUNCT
ejpam-6138	136	3	λ2	λ2	NOUN
ejpam-6138	136	4	−	−	PROPN
ejpam-6138	136	5	λ1	λ1	PROPN
ejpam-6138	136	6	)	)	PUNCT
ejpam-6138	136	7	(	(	PUNCT
ejpam-6138	136	8	τ	τ	X
ejpam-6138	136	9	ϑ	ϑ	X
ejpam-6138	136	10	)	)	PUNCT
ejpam-6138	136	11	ϱ	ϱ	PROPN
ejpam-6138	136	12	+	+	X
ejpam-6138	136	13	λ1	λ1	ADJ
ejpam-6138	136	14	]	]	X
ejpam-6138	136	15	+	+	NUM
ejpam-6138	136	16	∫	∫	PROPN
ejpam-6138	136	17	ϑ	ϑ	X
ejpam-6138	136	18	0	0	NUM
ejpam-6138	136	19	h̵(τ	h̵(τ	PROPN
ejpam-6138	136	20	,	,	PUNCT
ejpam-6138	136	21	r	r	NOUN
ejpam-6138	136	22	)	)	PUNCT
ejpam-6138	136	23	ξ	ξ	PROPN
ejpam-6138	136	24	(	(	PUNCT
ejpam-6138	136	25	r	r	NOUN
ejpam-6138	136	26	,	,	PUNCT
ejpam-6138	136	27	µ(r	µ(r	NOUN
ejpam-6138	136	28	)	)	PUNCT
ejpam-6138	136	29	,	,	PUNCT
ejpam-6138	136	30	ϱcdς	ϱcdς	ADJ
ejpam-6138	136	31	0+µ(r	0+µ(r	NOUN
ejpam-6138	136	32	)	)	PUNCT
ejpam-6138	136	33	)	)	PUNCT
ejpam-6138	137	1	dr	dr	PROPN
ejpam-6138	137	2	(	(	PUNCT
ejpam-6138	137	3	3.15	3.15	NUM
ejpam-6138	137	4	)	)	PUNCT
ejpam-6138	137	5	for	for	ADP
ejpam-6138	137	6	τ	τ	PROPN
ejpam-6138	137	7	∈	∈	PROPN
ejpam-6138	138	1	[	[	X
ejpam-6138	138	2	0	0	NUM
ejpam-6138	138	3	,	,	PUNCT
ejpam-6138	138	4	ϑ	ϑ	NOUN
ejpam-6138	138	5	]	]	X
ejpam-6138	138	6	.	.	PUNCT
ejpam-6138	139	1	we	we	PRON
ejpam-6138	139	2	should	should	AUX
ejpam-6138	139	3	interpret	interpret	VERB
ejpam-6138	139	4	that	that	SCONJ
ejpam-6138	139	5	the	the	DET
ejpam-6138	139	6	application	application	NOUN
ejpam-6138	139	7	σ	σ	PROPN
ejpam-6138	139	8	admits	admit	VERB
ejpam-6138	139	9	a	a	DET
ejpam-6138	139	10	single	single	ADJ
ejpam-6138	139	11	fixed	fix	VERB
ejpam-6138	139	12	point	point	NOUN
ejpam-6138	139	13	.	.	PUNCT
ejpam-6138	140	1	assume	assume	VERB
ejpam-6138	140	2	µ	µ	PRON
ejpam-6138	140	3	,	,	PUNCT
ejpam-6138	140	4	ν	ν	PROPN
ejpam-6138	140	5	∈	∈	PROPN
ejpam-6138	140	6	π	π	X
ejpam-6138	140	7	.	.	PUNCT
ejpam-6138	141	1	therefore	therefore	ADV
ejpam-6138	141	2	ζ∣σµ(τ	ζ∣σµ(τ	PROPN
ejpam-6138	141	3	)	)	PUNCT
ejpam-6138	141	4	−	−	NOUN
ejpam-6138	141	5	σν(τ)∣	σν(τ)∣	ADJ
ejpam-6138	141	6	≤	≤	NUM
ejpam-6138	141	7	∫	∫	PROPN
ejpam-6138	141	8	ϑ	ϑ	X
ejpam-6138	141	9	0	0	NUM
ejpam-6138	141	10	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	141	11	,	,	PUNCT
ejpam-6138	141	12	r)∣	r)∣	NOUN
ejpam-6138	141	13	∣ξ	∣ξ	PROPN
ejpam-6138	141	14	(	(	PUNCT
ejpam-6138	141	15	r	r	NOUN
ejpam-6138	141	16	,	,	PUNCT
ejpam-6138	141	17	µ(r	µ(r	NOUN
ejpam-6138	141	18	)	)	PUNCT
ejpam-6138	141	19	,	,	PUNCT
ejpam-6138	141	20	ϱcdς	ϱcdς	ADJ
ejpam-6138	141	21	0+µ(r	0+µ(r	NOUN
ejpam-6138	141	22	)	)	PUNCT
ejpam-6138	141	23	)	)	PUNCT
ejpam-6138	142	1	−	−	PROPN
ejpam-6138	142	2	ξ	ξ	X
ejpam-6138	142	3	(	(	PUNCT
ejpam-6138	142	4	r	r	NOUN
ejpam-6138	142	5	,	,	PUNCT
ejpam-6138	142	6	ν(r	ν(r	PROPN
ejpam-6138	142	7	)	)	PUNCT
ejpam-6138	142	8	,	,	PUNCT
ejpam-6138	142	9	ϱcdς	ϱcdς	NOUN
ejpam-6138	142	10	0+ν(r))∣	0+ν(r))∣	PROPN
ejpam-6138	142	11	dr	dr	PROPN
ejpam-6138	142	12	≤	≤	PROPN
ejpam-6138	142	13	∫	∫	PROPN
ejpam-6138	142	14	ϑ	ϑ	X
ejpam-6138	142	15	0	0	NUM
ejpam-6138	142	16	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	142	17	,	,	PUNCT
ejpam-6138	142	18	r)∣	r)∣	PROPN
ejpam-6138	142	19	(	(	PUNCT
ejpam-6138	142	20	ζ∣µ(τ	ζ∣µ(τ	PROPN
ejpam-6138	142	21	)	)	PUNCT
ejpam-6138	142	22	−	−	NOUN
ejpam-6138	142	23	ν(τ)∣	ν(τ)∣	NOUN
ejpam-6138	142	24	+	+	CCONJ
ejpam-6138	142	25	η∣µ′(τ	η∣µ′(τ	ADJ
ejpam-6138	142	26	)	)	PUNCT
ejpam-6138	142	27	−	−	ADP
ejpam-6138	142	28	ν	ν	NOUN
ejpam-6138	142	29	′(τ)∣	′(τ)∣	ADJ
ejpam-6138	142	30	)	)	PUNCT
ejpam-6138	142	31	dr	dr	PROPN
ejpam-6138	142	32	≤	≤	PROPN
ejpam-6138	142	33	ζ	ζ	PROPN
ejpam-6138	142	34	∫	∫	PROPN
ejpam-6138	142	35	ϑ	ϑ	X
ejpam-6138	142	36	0	0	NUM
ejpam-6138	142	37	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	142	38	,	,	PUNCT
ejpam-6138	142	39	r)∣dr∥µ	r)∣dr∥µ	PROPN
ejpam-6138	142	40	−	−	PROPN
ejpam-6138	142	41	ν∥	ν∥	NOUN
ejpam-6138	142	42	≤	≤	NUM
ejpam-6138	142	43	ζ	ζ	NOUN
ejpam-6138	142	44	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	142	45	)	)	PUNCT
ejpam-6138	142	46	[	[	PUNCT
ejpam-6138	142	47	ϑ	ϑ	PROPN
ejpam-6138	142	48	ϱσ	ϱσ	PROPN
ejpam-6138	142	49	σ	σ	PROPN
ejpam-6138	142	50	1	1	PROPN
ejpam-6138	142	51	/	/	SYM
ejpam-6138	142	52	σ−1	σ−1	PROPN
ejpam-6138	142	53	−	−	NOUN
ejpam-6138	142	54	ϑ	ϑ	PROPN
ejpam-6138	142	55	ϱσ	ϱσ	PROPN
ejpam-6138	142	56	σ	σ	PROPN
ejpam-6138	142	57	σ	σ	PROPN
ejpam-6138	142	58	/	/	SYM
ejpam-6138	142	59	σ−1	σ−1	PROPN
ejpam-6138	142	60	]	]	PUNCT
ejpam-6138	142	61	∥µ	∥µ	PROPN
ejpam-6138	142	62	−	−	PROPN
ejpam-6138	142	63	ν∥	ν∥	NOUN
ejpam-6138	142	64	,	,	PUNCT
ejpam-6138	142	65	for	for	ADP
ejpam-6138	142	66	τ	τ	PROPN
ejpam-6138	142	67	∈	∈	PROPN
ejpam-6138	143	1	[	[	X
ejpam-6138	143	2	0	0	NUM
ejpam-6138	143	3	,	,	PUNCT
ejpam-6138	143	4	ϑ	ϑ	X
ejpam-6138	143	5	]	]	X
ejpam-6138	143	6	,	,	PUNCT
ejpam-6138	143	7	and	and	CCONJ
ejpam-6138	143	8	similarly	similarly	ADV
ejpam-6138	143	9	,	,	PUNCT
ejpam-6138	143	10	η	η	NOUN
ejpam-6138	143	11	»	»	NOUN
ejpam-6138	143	12	»	»	ADV
ejpam-6138	143	13	»	»	PRON
ejpam-6138	143	14	»	»	PUNCT
ejpam-6138	143	15	»	»	PUNCT
ejpam-6138	143	16	(	(	PUNCT
ejpam-6138	143	17	σµ	σµ	NOUN
ejpam-6138	143	18	)	)	PUNCT
ejpam-6138	143	19	′(τ	′(τ	NOUN
ejpam-6138	143	20	)	)	PUNCT
ejpam-6138	143	21	−	−	PROPN
ejpam-6138	143	22	(	(	PUNCT
ejpam-6138	143	23	σν)′(τ	σν)′(τ	NOUN
ejpam-6138	143	24	)	)	PUNCT
ejpam-6138	143	25	»	»	NOUN
ejpam-6138	143	26	»	»	PUNCT
ejpam-6138	143	27	»	»	PRON
ejpam-6138	143	28	»	»	ADV
ejpam-6138	143	29	»	»	X
ejpam-6138	143	30	≤	≤	NUM
ejpam-6138	143	31	∫	∫	PROPN
ejpam-6138	143	32	1	1	NUM
ejpam-6138	143	33	0	0	NUM
ejpam-6138	143	34	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	143	35	,	,	PUNCT
ejpam-6138	143	36	r)∣	r)∣	NOUN
ejpam-6138	143	37	∂τ	∂τ	NOUN
ejpam-6138	143	38	∣ξ	∣ξ	PROPN
ejpam-6138	143	39	(	(	PUNCT
ejpam-6138	143	40	r	r	NOUN
ejpam-6138	143	41	,	,	PUNCT
ejpam-6138	143	42	µ(r	µ(r	NOUN
ejpam-6138	143	43	)	)	PUNCT
ejpam-6138	143	44	,	,	PUNCT
ejpam-6138	143	45	ϱcdς	ϱcdς	ADJ
ejpam-6138	143	46	0+µ(r	0+µ(r	NOUN
ejpam-6138	143	47	)	)	PUNCT
ejpam-6138	143	48	)	)	PUNCT
ejpam-6138	144	1	−	−	PROPN
ejpam-6138	144	2	ξ	ξ	X
ejpam-6138	144	3	(	(	PUNCT
ejpam-6138	144	4	r	r	NOUN
ejpam-6138	144	5	,	,	PUNCT
ejpam-6138	144	6	ν(r	ν(r	PROPN
ejpam-6138	144	7	)	)	PUNCT
ejpam-6138	144	8	,	,	PUNCT
ejpam-6138	144	9	ϱcdς	ϱcdς	NOUN
ejpam-6138	144	10	0+ν(r))∣	0+ν(r))∣	PROPN
ejpam-6138	144	11	dr	dr	PROPN
ejpam-6138	144	12	≤	≤	PROPN
ejpam-6138	144	13	∫	∫	PROPN
ejpam-6138	144	14	ϑ	ϑ	X
ejpam-6138	144	15	0	0	NUM
ejpam-6138	144	16	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	144	17	,	,	PUNCT
ejpam-6138	144	18	r)∣	r)∣	PROPN
ejpam-6138	144	19	∂τ	∂τ	PROPN
ejpam-6138	144	20	(	(	PUNCT
ejpam-6138	144	21	ζ∣µ(τ	ζ∣µ(τ	PROPN
ejpam-6138	144	22	)	)	PUNCT
ejpam-6138	144	23	−	−	NOUN
ejpam-6138	144	24	ν(τ)∣	ν(τ)∣	NOUN
ejpam-6138	144	25	+	+	CCONJ
ejpam-6138	144	26	η∣µ′(τ	η∣µ′(τ	ADJ
ejpam-6138	144	27	)	)	PUNCT
ejpam-6138	144	28	−	−	ADP
ejpam-6138	144	29	ν	ν	NOUN
ejpam-6138	144	30	′(τ)∣	′(τ)∣	ADJ
ejpam-6138	144	31	)	)	PUNCT
ejpam-6138	144	32	dr	dr	PROPN
ejpam-6138	144	33	≤	≤	NOUN
ejpam-6138	144	34	η∫	η∫	VERB
ejpam-6138	144	35	ϑ	ϑ	X
ejpam-6138	144	36	0	0	NUM
ejpam-6138	144	37	∣h̵(τ	∣h̵(τ	NOUN
ejpam-6138	144	38	,	,	PUNCT
ejpam-6138	144	39	r)∣	r)∣	NOUN
ejpam-6138	144	40	∂τ	∂τ	NOUN
ejpam-6138	144	41	dr∥µ	dr∥µ	PROPN
ejpam-6138	144	42	−	−	PROPN
ejpam-6138	144	43	ν∥	ν∥	NOUN
ejpam-6138	144	44	≤	≤	NUM
ejpam-6138	144	45	η	η	PROPN
ejpam-6138	144	46	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	144	47	)	)	PUNCT
ejpam-6138	145	1	[	[	X
ejpam-6138	145	2	ϑ	ϑ	X
ejpam-6138	145	3	ϱσ−1	ϱσ−1	PROPN
ejpam-6138	145	4	(	(	PUNCT
ejpam-6138	145	5	ϱ−1	ϱ−1	PROPN
ejpam-6138	145	6	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	145	7	)	)	PUNCT
ejpam-6138	145	8	)	)	PUNCT
ejpam-6138	145	9	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	145	10	)	)	PUNCT
ejpam-6138	145	11	−σ(ϑ)ϱσ−1	−σ(ϑ)ϱσ−1	NOUN
ejpam-6138	145	12	(	(	PUNCT
ejpam-6138	145	13	ϱ−1	ϱ−1	PROPN
ejpam-6138	145	14	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	145	15	)	)	PUNCT
ejpam-6138	145	16	)	)	PUNCT
ejpam-6138	145	17	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	145	18	)	)	PUNCT
ejpam-6138	145	19	]	]	X
ejpam-6138	145	20	∥µ	∥µ	PROPN
ejpam-6138	145	21	−	−	PROPN
ejpam-6138	145	22	ν∥	ν∥	NOUN
ejpam-6138	145	23	,	,	PUNCT
ejpam-6138	145	24	τ	τ	PROPN
ejpam-6138	145	25	∈	∈	PROPN
ejpam-6138	146	1	[	[	X
ejpam-6138	146	2	0	0	NUM
ejpam-6138	146	3	,	,	PUNCT
ejpam-6138	146	4	ϑ	ϑ	NOUN
ejpam-6138	146	5	]	]	X
ejpam-6138	146	6	.	.	PUNCT
ejpam-6138	147	1	hence	hence	ADV
ejpam-6138	147	2	,	,	PUNCT
ejpam-6138	147	3	∥σµ	∥σµ	NUM
ejpam-6138	147	4	−	−	NOUN
ejpam-6138	147	5	σν∥	σν∥	NOUN
ejpam-6138	147	6	≤	≤	NUM
ejpam-6138	147	7	ϖ∥µ	ϖ∥µ	VERB
ejpam-6138	147	8	−	−	PROPN
ejpam-6138	147	9	ν∥	ν∥	NOUN
ejpam-6138	147	10	,	,	PUNCT
ejpam-6138	147	11	where	where	SCONJ
ejpam-6138	147	12	ϖ	ϖ	NOUN
ejpam-6138	147	13	=	=	SYM
ejpam-6138	147	14	ζ	ζ	NOUN
ejpam-6138	147	15	ϱσγ(σ+1	ϱσγ(σ+1	PROPN
ejpam-6138	147	16	)	)	PUNCT
ejpam-6138	147	17	[	[	PUNCT
ejpam-6138	147	18	ϑ	ϑ	X
ejpam-6138	147	19	ϱσ	ϱσ	PROPN
ejpam-6138	147	20	σ	σ	PROPN
ejpam-6138	147	21	1/ϱ(σ−1	1/ϱ(σ−1	PROPN
ejpam-6138	147	22	)	)	PUNCT
ejpam-6138	147	23	−	−	PROPN
ejpam-6138	147	24	ϑ	ϑ	PROPN
ejpam-6138	147	25	ϱσ	ϱσ	PROPN
ejpam-6138	147	26	σ	σ	PROPN
ejpam-6138	147	27	σ	σ	PROPN
ejpam-6138	147	28	/	/	SYM
ejpam-6138	147	29	σ−1	σ−1	PROPN
ejpam-6138	147	30	]	]	PUNCT
ejpam-6138	148	1	+	+	CCONJ
ejpam-6138	148	2	η	η	PROPN
ejpam-6138	148	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	148	4	)	)	PUNCT
ejpam-6138	149	1	[	[	X
ejpam-6138	149	2	ϑ	ϑ	X
ejpam-6138	149	3	ϱσ−1	ϱσ−1	PROPN
ejpam-6138	149	4	(	(	PUNCT
ejpam-6138	149	5	ϱ−1	ϱ−1	PROPN
ejpam-6138	149	6	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	149	7	)	)	PUNCT
ejpam-6138	149	8	)	)	PUNCT
ejpam-6138	149	9	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	149	10	)	)	PUNCT
ejpam-6138	149	11	−σ(ϑ)ϱσ−1	−σ(ϑ)ϱσ−1	NOUN
ejpam-6138	149	12	(	(	PUNCT
ejpam-6138	149	13	ϱ−1	ϱ−1	PROPN
ejpam-6138	149	14	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	149	15	)	)	PUNCT
ejpam-6138	149	16	)	)	PUNCT
ejpam-6138	149	17	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	149	18	)	)	PUNCT
ejpam-6138	149	19	]	]	PUNCT
ejpam-6138	150	1	<	<	X
ejpam-6138	150	2	1	1	X
ejpam-6138	150	3	.	.	X
ejpam-6138	150	4	whither	whither	NOUN
ejpam-6138	150	5	,	,	PUNCT
ejpam-6138	150	6	we	we	PRON
ejpam-6138	150	7	have	have	AUX
ejpam-6138	150	8	martyred	martyr	VERB
ejpam-6138	150	9	proposition	proposition	NOUN
ejpam-6138	150	10	2	2	NUM
ejpam-6138	150	11	.	.	PUNCT
ejpam-6138	150	12	according	accord	VERB
ejpam-6138	150	13	to	to	ADP
ejpam-6138	150	14	(	(	PUNCT
ejpam-6138	150	15	3.12	3.12	NUM
ejpam-6138	150	16	)	)	PUNCT
ejpam-6138	150	17	,	,	PUNCT
ejpam-6138	150	18	we	we	PRON
ejpam-6138	150	19	extrapolate	extrapolate	VERB
ejpam-6138	150	20	that	that	SCONJ
ejpam-6138	150	21	σ	σ	PROPN
ejpam-6138	150	22	is	be	AUX
ejpam-6138	150	23	a	a	DET
ejpam-6138	150	24	contracting	contracting	NOUN
ejpam-6138	150	25	operator	operator	NOUN
ejpam-6138	150	26	on	on	ADP
ejpam-6138	150	27	π	π	PROPN
ejpam-6138	150	28	,	,	PUNCT
ejpam-6138	150	29	so	so	ADV
ejpam-6138	150	30	,	,	PUNCT
ejpam-6138	150	31	by	by	ADP
ejpam-6138	150	32	the	the	DET
ejpam-6138	150	33	theorem	theorem	NOUN
ejpam-6138	150	34	of	of	ADP
ejpam-6138	150	35	contraction	contraction	NOUN
ejpam-6138	150	36	mapping	mapping	NOUN
ejpam-6138	150	37	of	of	ADP
ejpam-6138	150	38	banach	banach	NOUN
ejpam-6138	150	39	we	we	PRON
ejpam-6138	150	40	culminate	culminate	VERB
ejpam-6138	150	41	in	in	ADP
ejpam-6138	150	42	the	the	DET
ejpam-6138	150	43	possible	possible	ADJ
ejpam-6138	150	44	outcome	outcome	NOUN
ejpam-6138	150	45	.	.	PUNCT
ejpam-6138	151	1	this	this	PRON
ejpam-6138	151	2	means	mean	VERB
ejpam-6138	151	3	that	that	SCONJ
ejpam-6138	151	4	,	,	PUNCT
ejpam-6138	151	5	we	we	PRON
ejpam-6138	151	6	conclude	conclude	VERB
ejpam-6138	151	7	that	that	SCONJ
ejpam-6138	151	8	σ	σ	PROPN
ejpam-6138	151	9	accepts	accept	VERB
ejpam-6138	151	10	a	a	DET
ejpam-6138	151	11	single	single	ADJ
ejpam-6138	151	12	fixed	fix	VERB
ejpam-6138	151	13	point	point	NOUN
ejpam-6138	151	14	in	in	ADP
ejpam-6138	151	15	c[0	c[0	PROPN
ejpam-6138	151	16	,	,	PUNCT
ejpam-6138	151	17	ϑ	ϑ	X
ejpam-6138	151	18	]	]	X
ejpam-6138	151	19	,	,	PUNCT
ejpam-6138	151	20	this	this	PRON
ejpam-6138	151	21	requires	require	VERB
ejpam-6138	151	22	that	that	SCONJ
ejpam-6138	151	23	the	the	DET
ejpam-6138	151	24	bvp	bvp	NOUN
ejpam-6138	151	25	(	(	PUNCT
ejpam-6138	151	26	3.13	3.13	NUM
ejpam-6138	151	27	)	)	PUNCT
ejpam-6138	151	28	admits	admit	VERB
ejpam-6138	151	29	a	a	DET
ejpam-6138	151	30	single	single	ADJ
ejpam-6138	151	31	solution	solution	NOUN
ejpam-6138	151	32	.	.	PUNCT
ejpam-6138	152	1	z.	z.	PROPN
ejpam-6138	152	2	bekri	bekri	PROPN
ejpam-6138	152	3	et	et	PROPN
ejpam-6138	152	4	al	al	PROPN
ejpam-6138	152	5	.	.	PUNCT
ejpam-6138	152	6	/	/	SYM
ejpam-6138	152	7	eur	eur	PROPN
ejpam-6138	152	8	.	.	PUNCT
ejpam-6138	153	1	j.	j.	PROPN
ejpam-6138	153	2	pure	pure	PROPN
ejpam-6138	153	3	appl	appl	PROPN
ejpam-6138	153	4	.	.	PROPN
ejpam-6138	153	5	math	math	PROPN
ejpam-6138	153	6	,	,	PUNCT
ejpam-6138	153	7	18	18	NUM
ejpam-6138	153	8	(	(	PUNCT
ejpam-6138	153	9	2	2	NUM
ejpam-6138	153	10	)	)	PUNCT
ejpam-6138	153	11	(	(	PUNCT
ejpam-6138	153	12	2025	2025	NUM
ejpam-6138	153	13	)	)	PUNCT
ejpam-6138	153	14	,	,	PUNCT
ejpam-6138	153	15	6138	6138	NUM
ejpam-6138	153	16	8	8	NUM
ejpam-6138	153	17	of	of	ADP
ejpam-6138	153	18	17	17	NUM
ejpam-6138	153	19	remark	remark	NOUN
ejpam-6138	153	20	1	1	NUM
ejpam-6138	153	21	.	.	PUNCT
ejpam-6138	154	1	we	we	PRON
ejpam-6138	154	2	analyze	analyze	VERB
ejpam-6138	154	3	this	this	PRON
ejpam-6138	154	4	when	when	SCONJ
ejpam-6138	154	5	taking	take	VERB
ejpam-6138	154	6	σ	σ	X
ejpam-6138	154	7	=	=	SYM
ejpam-6138	154	8	2	2	NUM
ejpam-6138	154	9	,	,	PUNCT
ejpam-6138	154	10	ς	ς	PROPN
ejpam-6138	154	11	=	=	SYM
ejpam-6138	154	12	1	1	NUM
ejpam-6138	154	13	,	,	PUNCT
ejpam-6138	154	14	θ	θ	PROPN
ejpam-6138	154	15	=	=	SYM
ejpam-6138	154	16	0	0	NUM
ejpam-6138	154	17	and	and	CCONJ
ejpam-6138	154	18	ϱ	ϱ	X
ejpam-6138	154	19	=	=	SYM
ejpam-6138	154	20	1	1	NUM
ejpam-6138	154	21	in	in	ADP
ejpam-6138	154	22	theorem	theorem	NOUN
ejpam-6138	154	23	2	2	NUM
ejpam-6138	154	24	,	,	PUNCT
ejpam-6138	154	25	through	through	ADP
ejpam-6138	154	26	condition	condition	NOUN
ejpam-6138	154	27	(	(	PUNCT
ejpam-6138	154	28	3.12	3.12	NUM
ejpam-6138	154	29	)	)	PUNCT
ejpam-6138	154	30	,	,	PUNCT
ejpam-6138	154	31	we	we	PRON
ejpam-6138	154	32	obviously	obviously	ADV
ejpam-6138	154	33	find	find	VERB
ejpam-6138	154	34	theorem	theorem	VERB
ejpam-6138	154	35	1	1	NUM
ejpam-6138	154	36	such	such	ADJ
ejpam-6138	154	37	that	that	SCONJ
ejpam-6138	154	38	ζ	ζ	PROPN
ejpam-6138	154	39	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	154	40	)	)	PUNCT
ejpam-6138	154	41	[	[	PUNCT
ejpam-6138	154	42	ϑ	ϑ	PROPN
ejpam-6138	154	43	ϱσ	ϱσ	PROPN
ejpam-6138	154	44	σ	σ	PROPN
ejpam-6138	154	45	1	1	PROPN
ejpam-6138	154	46	/	/	SYM
ejpam-6138	155	1	σ−1	σ−1	PROPN
ejpam-6138	155	2	−	−	NOUN
ejpam-6138	155	3	ϑ	ϑ	PROPN
ejpam-6138	155	4	ϱσ	ϱσ	PROPN
ejpam-6138	155	5	σ	σ	PROPN
ejpam-6138	155	6	σ	σ	PROPN
ejpam-6138	155	7	/	/	PROPN
ejpam-6138	155	8	σ−1	σ−1	PROPN
ejpam-6138	155	9	]	]	PUNCT
ejpam-6138	156	1	+	+	NUM
ejpam-6138	156	2	η	η	X
ejpam-6138	156	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	156	4	)	)	PUNCT
ejpam-6138	157	1	[	[	X
ejpam-6138	157	2	ϑ	ϑ	X
ejpam-6138	157	3	ϱσ−1	ϱσ−1	PROPN
ejpam-6138	157	4	(	(	PUNCT
ejpam-6138	157	5	ϱ−1	ϱ−1	PROPN
ejpam-6138	157	6	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	157	7	)	)	PUNCT
ejpam-6138	157	8	)	)	PUNCT
ejpam-6138	157	9	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	157	10	)	)	PUNCT
ejpam-6138	157	11	−σ(ϑ)ϱσ−1	−σ(ϑ)ϱσ−1	NOUN
ejpam-6138	157	12	(	(	PUNCT
ejpam-6138	157	13	ϱ−1	ϱ−1	PROPN
ejpam-6138	157	14	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	157	15	)	)	PUNCT
ejpam-6138	157	16	)	)	PUNCT
ejpam-6138	157	17	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	157	18	)	)	PUNCT
ejpam-6138	157	19	]	]	PUNCT
ejpam-6138	158	1	=	=	PUNCT
ejpam-6138	158	2	ζ	ζ	X
ejpam-6138	158	3	ϑ	ϑ	PROPN
ejpam-6138	158	4	2	2	NUM
ejpam-6138	158	5	4γ(3	4γ(3	NUM
ejpam-6138	158	6	)	)	PUNCT
ejpam-6138	159	1	+	+	CCONJ
ejpam-6138	159	2	η	η	PROPN
ejpam-6138	159	3	ϑ	ϑ	X
ejpam-6138	159	4	γ(3	γ(3	PROPN
ejpam-6138	159	5	)	)	PUNCT
ejpam-6138	159	6	<	<	X
ejpam-6138	159	7	1	1	X
ejpam-6138	159	8	.	.	PUNCT
ejpam-6138	159	9	proposition	proposition	NOUN
ejpam-6138	159	10	3	3	NUM
ejpam-6138	159	11	(	(	PUNCT
ejpam-6138	159	12	[	[	X
ejpam-6138	159	13	17	17	NUM
ejpam-6138	159	14	]	]	PUNCT
ejpam-6138	159	15	)	)	PUNCT
ejpam-6138	159	16	.	.	PUNCT
ejpam-6138	160	1	by	by	ADP
ejpam-6138	160	2	(	(	PUNCT
ejpam-6138	160	3	3.3	3.3	NUM
ejpam-6138	160	4	)	)	PUNCT
ejpam-6138	160	5	and	and	CCONJ
ejpam-6138	160	6	(	(	PUNCT
ejpam-6138	160	7	3.4	3.4	NUM
ejpam-6138	160	8	)	)	PUNCT
ejpam-6138	160	9	,	,	PUNCT
ejpam-6138	160	10	suppose	suppose	VERB
ejpam-6138	160	11	that	that	SCONJ
ejpam-6138	160	12	θ	θ	PROPN
ejpam-6138	160	13	=	=	SYM
ejpam-6138	160	14	0	0	NUM
ejpam-6138	160	15	,	,	PUNCT
ejpam-6138	160	16	ϑ	ϑ	X
ejpam-6138	160	17	=	=	SYM
ejpam-6138	160	18	1	1	NUM
ejpam-6138	160	19	then	then	ADV
ejpam-6138	160	20	∫	∫	PROPN
ejpam-6138	160	21	1	1	NUM
ejpam-6138	160	22	0	0	NUM
ejpam-6138	160	23	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	160	24	,	,	PUNCT
ejpam-6138	160	25	r)∣dr	r)∣dr	X
ejpam-6138	160	26	≤	≤	ADV
ejpam-6138	160	27	1	1	NUM
ejpam-6138	160	28	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	160	29	)	)	PUNCT
ejpam-6138	160	30	[	[	PUNCT
ejpam-6138	160	31	1	1	NUM
ejpam-6138	160	32	σ	σ	NUM
ejpam-6138	160	33	1/ϱ(σ−1	1/ϱ(σ−1	NUM
ejpam-6138	160	34	)	)	PUNCT
ejpam-6138	160	35	−	−	PROPN
ejpam-6138	160	36	1	1	NUM
ejpam-6138	160	37	σσ/(σ−1	σσ/(σ−1	NUM
ejpam-6138	160	38	)	)	PUNCT
ejpam-6138	160	39	]	]	PUNCT
ejpam-6138	160	40	,	,	PUNCT
ejpam-6138	160	41	(	(	PUNCT
ejpam-6138	160	42	3.16	3.16	NUM
ejpam-6138	160	43	)	)	PUNCT
ejpam-6138	160	44	and	and	CCONJ
ejpam-6138	160	45	∫	∫	PROPN
ejpam-6138	160	46	1	1	NUM
ejpam-6138	160	47	0	0	NUM
ejpam-6138	160	48	∂∣h̵(τ	∂∣h̵(τ	PROPN
ejpam-6138	160	49	,	,	PUNCT
ejpam-6138	160	50	r)∣	r)∣	PROPN
ejpam-6138	160	51	∂τ	∂τ	PROPN
ejpam-6138	160	52	dr	dr	PROPN
ejpam-6138	160	53	≤	≤	PROPN
ejpam-6138	160	54	1	1	NUM
ejpam-6138	160	55	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	NOUN
ejpam-6138	160	56	)	)	PUNCT
ejpam-6138	161	1	[	[	X
ejpam-6138	161	2	(	(	PUNCT
ejpam-6138	161	3	ϱ−1	ϱ−1	PROPN
ejpam-6138	161	4	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	161	5	)	)	PUNCT
ejpam-6138	161	6	)	)	PUNCT
ejpam-6138	161	7	(	(	PUNCT
ejpam-6138	161	8	ϱ−1)/ϱ(σ−1	ϱ−1)/ϱ(σ−1	NOUN
ejpam-6138	161	9	)	)	PUNCT
ejpam-6138	161	10	−	−	PROPN
ejpam-6138	161	11	σ	σ	NOUN
ejpam-6138	161	12	(	(	PUNCT
ejpam-6138	161	13	ϱ−1	ϱ−1	PROPN
ejpam-6138	161	14	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	161	15	)	)	PUNCT
ejpam-6138	161	16	)	)	PUNCT
ejpam-6138	161	17	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	161	18	)	)	PUNCT
ejpam-6138	161	19	]	]	PUNCT
ejpam-6138	161	20	.	.	PUNCT
ejpam-6138	162	1	(	(	PUNCT
ejpam-6138	162	2	3.17	3.17	NUM
ejpam-6138	162	3	)	)	PUNCT
ejpam-6138	162	4	theorem	theorem	NOUN
ejpam-6138	162	5	3	3	NUM
ejpam-6138	162	6	(	(	PUNCT
ejpam-6138	162	7	[	[	X
ejpam-6138	162	8	17	17	NUM
ejpam-6138	162	9	]	]	NUM
ejpam-6138	162	10	)	)	PUNCT
ejpam-6138	162	11	.	.	PUNCT
ejpam-6138	163	1	assume	assume	VERB
ejpam-6138	163	2	ξ	ξ	X
ejpam-6138	164	1	∶	∶	NOUN
ejpam-6138	165	1	[	[	X
ejpam-6138	165	2	0	0	NUM
ejpam-6138	165	3	,	,	PUNCT
ejpam-6138	165	4	1	1	NUM
ejpam-6138	165	5	]	]	SYM
ejpam-6138	165	6	×	×	NOUN
ejpam-6138	165	7	r2	r2	NOUN
ejpam-6138	165	8	→	→	PUNCT
ejpam-6138	165	9	r	r	NOUN
ejpam-6138	165	10	is	be	AUX
ejpam-6138	165	11	a	a	DET
ejpam-6138	165	12	function	function	NOUN
ejpam-6138	165	13	is	be	AUX
ejpam-6138	165	14	continuous	continuous	ADJ
ejpam-6138	165	15	and	and	CCONJ
ejpam-6138	165	16	check	check	VERB
ejpam-6138	165	17	a	a	DET
ejpam-6138	165	18	condition	condition	NOUN
ejpam-6138	165	19	of	of	ADP
ejpam-6138	165	20	uniform	uniform	ADJ
ejpam-6138	165	21	lipschitz	lipschitz	NOUN
ejpam-6138	165	22	concerning	concern	VERB
ejpam-6138	165	23	the	the	DET
ejpam-6138	165	24	second	second	ADJ
ejpam-6138	165	25	variable	variable	NOUN
ejpam-6138	165	26	on	on	ADP
ejpam-6138	165	27	[	[	X
ejpam-6138	165	28	0	0	NUM
ejpam-6138	165	29	,	,	PUNCT
ejpam-6138	165	30	1]×r2	1]×r2	NUM
ejpam-6138	165	31	with	with	ADP
ejpam-6138	165	32	lipschitz	lipschitz	VERB
ejpam-6138	165	33	real	real	ADJ
ejpam-6138	165	34	ζ	ζ	NOUN
ejpam-6138	165	35	,	,	PUNCT
ejpam-6138	165	36	thus	thus	ADV
ejpam-6138	165	37	,	,	PUNCT
ejpam-6138	165	38	»	»	PUNCT
ejpam-6138	165	39	»	»	PUNCT
ejpam-6138	165	40	»	»	PUNCT
ejpam-6138	165	41	»	»	PUNCT
ejpam-6138	165	42	»	»	PUNCT
ejpam-6138	165	43	»	»	X
ejpam-6138	165	44	ξ	ξ	X
ejpam-6138	165	45	(	(	PUNCT
ejpam-6138	165	46	τ	τ	PROPN
ejpam-6138	165	47	,	,	PUNCT
ejpam-6138	165	48	µ	µ	NOUN
ejpam-6138	165	49	,	,	PUNCT
ejpam-6138	165	50	µ′	µ′	NUM
ejpam-6138	165	51	)	)	PUNCT
ejpam-6138	165	52	−	−	PROPN
ejpam-6138	165	53	ξ	ξ	X
ejpam-6138	165	54	(	(	PUNCT
ejpam-6138	165	55	τ	τ	PROPN
ejpam-6138	165	56	,	,	PUNCT
ejpam-6138	165	57	ν	ν	PROPN
ejpam-6138	165	58	,	,	PUNCT
ejpam-6138	165	59	ν	ν	NOUN
ejpam-6138	165	60	′	′	NOUN
ejpam-6138	165	61	)	)	PUNCT
ejpam-6138	166	1	»	»	PRON
ejpam-6138	166	2	»	»	PUNCT
ejpam-6138	166	3	»	»	PUNCT
ejpam-6138	166	4	»	»	PRON
ejpam-6138	166	5	»	»	ADV
ejpam-6138	166	6	»	»	X
ejpam-6138	166	7	≤	≤	X
ejpam-6138	166	8	ζ∣µ	ζ∣µ	PUNCT
ejpam-6138	166	9	−	−	PROPN
ejpam-6138	166	10	ν∣	ν∣	NOUN
ejpam-6138	166	11	+	+	PUNCT
ejpam-6138	166	12	η∣µ′	η∣µ′	NOUN
ejpam-6138	166	13	−	−	NOUN
ejpam-6138	166	14	ν	ν	NOUN
ejpam-6138	166	15	′∣	′∣	PROPN
ejpam-6138	166	16	,	,	PUNCT
ejpam-6138	166	17	(	(	PUNCT
ejpam-6138	166	18	3.18	3.18	NUM
ejpam-6138	166	19	)	)	PUNCT
ejpam-6138	166	20	for	for	ADP
ejpam-6138	166	21	(	(	PUNCT
ejpam-6138	166	22	τ	τ	PROPN
ejpam-6138	166	23	,	,	PUNCT
ejpam-6138	166	24	µ	µ	NOUN
ejpam-6138	166	25	,	,	PUNCT
ejpam-6138	166	26	µ′	µ′	NOUN
ejpam-6138	166	27	)	)	PUNCT
ejpam-6138	166	28	,	,	PUNCT
ejpam-6138	166	29	(	(	PUNCT
ejpam-6138	166	30	τ	τ	X
ejpam-6138	166	31	,	,	PUNCT
ejpam-6138	166	32	ν	ν	PROPN
ejpam-6138	166	33	,	,	PUNCT
ejpam-6138	166	34	ν	ν	NOUN
ejpam-6138	166	35	′	′	NOUN
ejpam-6138	166	36	)	)	PUNCT
ejpam-6138	166	37	∈	∈	PROPN
ejpam-6138	167	1	[	[	X
ejpam-6138	167	2	0	0	NUM
ejpam-6138	167	3	,	,	PUNCT
ejpam-6138	167	4	1	1	NUM
ejpam-6138	167	5	]	]	SYM
ejpam-6138	167	6	×	×	NOUN
ejpam-6138	167	7	r2	r2	NOUN
ejpam-6138	167	8	,	,	PUNCT
ejpam-6138	167	9	where	where	SCONJ
ejpam-6138	167	10	η	η	PROPN
ejpam-6138	167	11	≥	≥	X
ejpam-6138	167	12	0	0	NUM
ejpam-6138	167	13	,	,	PUNCT
ejpam-6138	167	14	ζ	ζ	NOUN
ejpam-6138	167	15	>	>	SYM
ejpam-6138	167	16	0	0	NUM
ejpam-6138	167	17	are	be	AUX
ejpam-6138	167	18	constants	constant	NOUN
ejpam-6138	167	19	.	.	PUNCT
ejpam-6138	168	1	if	if	SCONJ
ejpam-6138	168	2	ζ	ζ	NOUN
ejpam-6138	168	3	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	168	4	)	)	PUNCT
ejpam-6138	168	5	[	[	PUNCT
ejpam-6138	168	6	1	1	NUM
ejpam-6138	168	7	σ	σ	NUM
ejpam-6138	168	8	1	1	NUM
ejpam-6138	168	9	/	/	SYM
ejpam-6138	168	10	σ−1	σ−1	NUM
ejpam-6138	168	11	−	−	NOUN
ejpam-6138	168	12	1	1	NUM
ejpam-6138	168	13	σ	σ	PROPN
ejpam-6138	168	14	σ	σ	PROPN
ejpam-6138	168	15	/	/	SYM
ejpam-6138	168	16	σ−1	σ−1	PROPN
ejpam-6138	168	17	]	]	PUNCT
ejpam-6138	169	1	+	+	CCONJ
ejpam-6138	169	2	η	η	PROPN
ejpam-6138	169	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	169	4	)	)	PUNCT
ejpam-6138	170	1	[	[	X
ejpam-6138	170	2	(	(	PUNCT
ejpam-6138	170	3	ϱ−1	ϱ−1	PROPN
ejpam-6138	170	4	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	170	5	)	)	PUNCT
ejpam-6138	170	6	)	)	PUNCT
ejpam-6138	170	7	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	170	8	)	)	PUNCT
ejpam-6138	170	9	−	−	PROPN
ejpam-6138	170	10	σ	σ	NOUN
ejpam-6138	170	11	(	(	PUNCT
ejpam-6138	170	12	ϱ−1	ϱ−1	PROPN
ejpam-6138	170	13	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	170	14	)	)	PUNCT
ejpam-6138	170	15	)	)	PUNCT
ejpam-6138	170	16	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	170	17	)	)	PUNCT
ejpam-6138	170	18	]	]	PUNCT
ejpam-6138	171	1	<	<	X
ejpam-6138	171	2	1	1	NUM
ejpam-6138	171	3	,	,	PUNCT
ejpam-6138	171	4	(	(	PUNCT
ejpam-6138	171	5	3.19	3.19	NUM
ejpam-6138	171	6	)	)	PUNCT
ejpam-6138	171	7	then	then	ADV
ejpam-6138	171	8	the	the	DET
ejpam-6138	171	9	bvp	bvp	PROPN
ejpam-6138	171	10	{	{	PUNCT
ejpam-6138	171	11	ϱ	ϱ	PROPN
ejpam-6138	171	12	cd	cd	PROPN
ejpam-6138	171	13	σ	σ	PROPN
ejpam-6138	171	14	0+µ(τ	0+µ(τ	PROPN
ejpam-6138	171	15	)	)	PUNCT
ejpam-6138	171	16	=	=	SYM
ejpam-6138	171	17	−ξ	−ξ	NOUN
ejpam-6138	171	18	(	(	PUNCT
ejpam-6138	171	19	τ	τ	PROPN
ejpam-6138	171	20	,	,	PUNCT
ejpam-6138	171	21	µ(τ	µ(τ	PROPN
ejpam-6138	171	22	)	)	PUNCT
ejpam-6138	171	23	,	,	PUNCT
ejpam-6138	171	24	ϱcdς	ϱcdς	ADJ
ejpam-6138	171	25	0+µ(τ	0+µ(τ	NOUN
ejpam-6138	171	26	)	)	PUNCT
ejpam-6138	171	27	)	)	PUNCT
ejpam-6138	171	28	,	,	PUNCT
ejpam-6138	171	29	0	0	PUNCT
ejpam-6138	171	30	<	<	X
ejpam-6138	171	31	τ	τ	X
ejpam-6138	171	32	<	<	X
ejpam-6138	171	33	1	1	NUM
ejpam-6138	171	34	,	,	PUNCT
ejpam-6138	171	35	µ(0	µ(0	NOUN
ejpam-6138	171	36	)	)	PUNCT
ejpam-6138	171	37	=	=	SYM
ejpam-6138	171	38	λ1	λ1	PROPN
ejpam-6138	171	39	,	,	PUNCT
ejpam-6138	171	40	µ(1	µ(1	PROPN
ejpam-6138	171	41	)	)	PUNCT
ejpam-6138	171	42	=	=	SYM
ejpam-6138	171	43	λ2	λ2	NOUN
ejpam-6138	171	44	,	,	PUNCT
ejpam-6138	171	45	(	(	PUNCT
ejpam-6138	171	46	3.20	3.20	NUM
ejpam-6138	171	47	)	)	PUNCT
ejpam-6138	171	48	has	have	VERB
ejpam-6138	171	49	a	a	DET
ejpam-6138	171	50	unique	unique	ADJ
ejpam-6138	171	51	solution	solution	NOUN
ejpam-6138	171	52	.	.	PUNCT
ejpam-6138	172	1	proof	proof	NOUN
ejpam-6138	172	2	.	.	PUNCT
ejpam-6138	173	1	using	use	VERB
ejpam-6138	173	2	the	the	DET
ejpam-6138	173	3	same	same	ADJ
ejpam-6138	173	4	method	method	NOUN
ejpam-6138	173	5	to	to	PART
ejpam-6138	173	6	prove	prove	VERB
ejpam-6138	173	7	proposition	proposition	NOUN
ejpam-6138	173	8	3	3	NUM
ejpam-6138	173	9	and	and	CCONJ
ejpam-6138	173	10	theorem	theorem	VERB
ejpam-6138	173	11	3	3	NUM
ejpam-6138	173	12	which	which	PRON
ejpam-6138	173	13	are	be	AUX
ejpam-6138	173	14	used	use	VERB
ejpam-6138	173	15	in	in	ADP
ejpam-6138	173	16	theorem	theorem	ADJ
ejpam-6138	173	17	2	2	NUM
ejpam-6138	173	18	and	and	CCONJ
ejpam-6138	173	19	proposition	proposition	NOUN
ejpam-6138	173	20	2	2	NUM
ejpam-6138	173	21	.	.	NOUN
ejpam-6138	173	22	remark	remark	NOUN
ejpam-6138	173	23	2	2	NUM
ejpam-6138	173	24	.	.	PUNCT
ejpam-6138	174	1	the	the	DET
ejpam-6138	174	2	same	same	ADJ
ejpam-6138	174	3	remark	remark	NOUN
ejpam-6138	174	4	1	1	NUM
ejpam-6138	174	5	,	,	PUNCT
ejpam-6138	174	6	we	we	PRON
ejpam-6138	174	7	notice	notice	VERB
ejpam-6138	174	8	that	that	SCONJ
ejpam-6138	174	9	when	when	SCONJ
ejpam-6138	174	10	σ	σ	PROPN
ejpam-6138	174	11	=	=	SYM
ejpam-6138	174	12	2	2	NUM
ejpam-6138	174	13	,	,	PUNCT
ejpam-6138	174	14	ς	ς	PROPN
ejpam-6138	174	15	=	=	SYM
ejpam-6138	174	16	1	1	NUM
ejpam-6138	174	17	,	,	PUNCT
ejpam-6138	174	18	θ	θ	PROPN
ejpam-6138	174	19	=	=	SYM
ejpam-6138	174	20	0	0	NUM
ejpam-6138	174	21	,	,	PUNCT
ejpam-6138	174	22	ϑ	ϑ	X
ejpam-6138	174	23	=	=	SYM
ejpam-6138	174	24	1	1	NUM
ejpam-6138	174	25	and	and	CCONJ
ejpam-6138	174	26	ϱ	ϱ	X
ejpam-6138	174	27	=	=	SYM
ejpam-6138	174	28	1	1	NUM
ejpam-6138	174	29	in	in	ADP
ejpam-6138	174	30	theorem	theorem	NOUN
ejpam-6138	174	31	3	3	NUM
ejpam-6138	174	32	,	,	PUNCT
ejpam-6138	174	33	through	through	ADP
ejpam-6138	174	34	condition	condition	NOUN
ejpam-6138	174	35	(	(	PUNCT
ejpam-6138	174	36	3.19	3.19	NUM
ejpam-6138	174	37	)	)	PUNCT
ejpam-6138	174	38	,	,	PUNCT
ejpam-6138	174	39	we	we	PRON
ejpam-6138	174	40	obviously	obviously	ADV
ejpam-6138	174	41	find	find	VERB
ejpam-6138	174	42	theorem	theorem	VERB
ejpam-6138	174	43	1	1	NUM
ejpam-6138	174	44	such	such	ADJ
ejpam-6138	174	45	that	that	SCONJ
ejpam-6138	174	46	ζ	ζ	PROPN
ejpam-6138	174	47	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	174	48	)	)	PUNCT
ejpam-6138	174	49	[	[	PUNCT
ejpam-6138	174	50	1	1	NUM
ejpam-6138	174	51	σ	σ	NUM
ejpam-6138	174	52	1	1	NUM
ejpam-6138	174	53	/	/	SYM
ejpam-6138	174	54	σ−1	σ−1	NUM
ejpam-6138	174	55	−	−	NOUN
ejpam-6138	174	56	1	1	NUM
ejpam-6138	174	57	σ	σ	PROPN
ejpam-6138	174	58	σ	σ	PROPN
ejpam-6138	174	59	/	/	SYM
ejpam-6138	174	60	σ−1	σ−1	PROPN
ejpam-6138	174	61	]	]	PUNCT
ejpam-6138	175	1	+	+	CCONJ
ejpam-6138	175	2	η	η	PROPN
ejpam-6138	175	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	175	4	)	)	PUNCT
ejpam-6138	176	1	[	[	X
ejpam-6138	176	2	(	(	PUNCT
ejpam-6138	176	3	ϱ−1	ϱ−1	PROPN
ejpam-6138	176	4	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	176	5	)	)	PUNCT
ejpam-6138	176	6	)	)	PUNCT
ejpam-6138	176	7	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	176	8	)	)	PUNCT
ejpam-6138	176	9	−	−	PROPN
ejpam-6138	176	10	σ	σ	NOUN
ejpam-6138	176	11	(	(	PUNCT
ejpam-6138	176	12	ϱ−1	ϱ−1	PROPN
ejpam-6138	176	13	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	176	14	)	)	PUNCT
ejpam-6138	176	15	)	)	PUNCT
ejpam-6138	176	16	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	176	17	)	)	PUNCT
ejpam-6138	176	18	]	]	PUNCT
ejpam-6138	177	1	=	=	PUNCT
ejpam-6138	177	2	ζ	ζ	SYM
ejpam-6138	177	3	1	1	NUM
ejpam-6138	177	4	4γ(3	4γ(3	NUM
ejpam-6138	177	5	)	)	PUNCT
ejpam-6138	178	1	+	+	CCONJ
ejpam-6138	178	2	η	η	PROPN
ejpam-6138	178	3	1	1	NUM
ejpam-6138	178	4	γ(3	γ(3	PROPN
ejpam-6138	178	5	)	)	PUNCT
ejpam-6138	178	6	<	<	X
ejpam-6138	179	1	1	1	X
ejpam-6138	179	2	.	.	PUNCT
ejpam-6138	179	3	z.	z.	PROPN
ejpam-6138	179	4	bekri	bekri	PROPN
ejpam-6138	179	5	et	et	PROPN
ejpam-6138	179	6	al	al	PROPN
ejpam-6138	179	7	.	.	PUNCT
ejpam-6138	179	8	/	/	SYM
ejpam-6138	179	9	eur	eur	PROPN
ejpam-6138	179	10	.	.	PUNCT
ejpam-6138	180	1	j.	j.	PROPN
ejpam-6138	180	2	pure	pure	PROPN
ejpam-6138	180	3	appl	appl	PROPN
ejpam-6138	180	4	.	.	PROPN
ejpam-6138	180	5	math	math	PROPN
ejpam-6138	180	6	,	,	PUNCT
ejpam-6138	180	7	18	18	NUM
ejpam-6138	180	8	(	(	PUNCT
ejpam-6138	180	9	2	2	NUM
ejpam-6138	180	10	)	)	PUNCT
ejpam-6138	180	11	(	(	PUNCT
ejpam-6138	180	12	2025	2025	NUM
ejpam-6138	180	13	)	)	PUNCT
ejpam-6138	180	14	,	,	PUNCT
ejpam-6138	180	15	6138	6138	NUM
ejpam-6138	180	16	9	9	NUM
ejpam-6138	180	17	of	of	ADP
ejpam-6138	180	18	17	17	NUM
ejpam-6138	180	19	proposition	proposition	NOUN
ejpam-6138	180	20	4	4	NUM
ejpam-6138	180	21	(	(	PUNCT
ejpam-6138	180	22	[	[	X
ejpam-6138	180	23	17	17	NUM
ejpam-6138	180	24	]	]	PUNCT
ejpam-6138	180	25	)	)	PUNCT
ejpam-6138	180	26	.	.	PUNCT
ejpam-6138	181	1	by	by	ADP
ejpam-6138	181	2	(	(	PUNCT
ejpam-6138	181	3	3.3	3.3	NUM
ejpam-6138	181	4	)	)	PUNCT
ejpam-6138	181	5	and	and	CCONJ
ejpam-6138	181	6	(	(	PUNCT
ejpam-6138	181	7	3.4	3.4	NUM
ejpam-6138	181	8	)	)	PUNCT
ejpam-6138	181	9	,	,	PUNCT
ejpam-6138	181	10	suppose	suppose	VERB
ejpam-6138	181	11	that	that	SCONJ
ejpam-6138	181	12	θ	θ	PROPN
ejpam-6138	181	13	<	<	X
ejpam-6138	181	14	ϑ	ϑ	X
ejpam-6138	181	15	then	then	ADV
ejpam-6138	181	16	∫	∫	PROPN
ejpam-6138	181	17	ϑ	ϑ	X
ejpam-6138	181	18	0	0	NUM
ejpam-6138	181	19	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	181	20	,	,	PUNCT
ejpam-6138	181	21	r)∣dr	r)∣dr	X
ejpam-6138	181	22	≤	≤	ADV
ejpam-6138	181	23	1	1	NUM
ejpam-6138	181	24	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	181	25	)	)	PUNCT
ejpam-6138	181	26	[	[	PUNCT
ejpam-6138	181	27	(	(	PUNCT
ejpam-6138	181	28	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-6138	181	29	σ	σ	PROPN
ejpam-6138	181	30	1	1	PROPN
ejpam-6138	181	31	/	/	SYM
ejpam-6138	181	32	σ−1	σ−1	NUM
ejpam-6138	181	33	−	−	PROPN
ejpam-6138	181	34	(	(	PUNCT
ejpam-6138	181	35	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-6138	181	36	σ	σ	PROPN
ejpam-6138	181	37	σ	σ	PROPN
ejpam-6138	181	38	/	/	SYM
ejpam-6138	181	39	σ−1	σ−1	PROPN
ejpam-6138	181	40	]	]	PUNCT
ejpam-6138	181	41	,	,	PUNCT
ejpam-6138	181	42	(	(	PUNCT
ejpam-6138	181	43	3.21	3.21	NUM
ejpam-6138	181	44	)	)	PUNCT
ejpam-6138	181	45	and	and	CCONJ
ejpam-6138	181	46	∫	∫	PROPN
ejpam-6138	181	47	ϑ	ϑ	X
ejpam-6138	181	48	0	0	NUM
ejpam-6138	181	49	∂∣h̵(τ	∂∣h̵(τ	PROPN
ejpam-6138	181	50	,	,	PUNCT
ejpam-6138	181	51	r)∣	r)∣	PROPN
ejpam-6138	181	52	∂τ	∂τ	PROPN
ejpam-6138	181	53	dr	dr	PROPN
ejpam-6138	181	54	≤	≤	PROPN
ejpam-6138	181	55	1	1	NUM
ejpam-6138	181	56	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	NOUN
ejpam-6138	181	57	)	)	PUNCT
ejpam-6138	182	1	[	[	X
ejpam-6138	182	2	(	(	PUNCT
ejpam-6138	182	3	ϑ	ϑ	X
ejpam-6138	182	4	−	−	PROPN
ejpam-6138	182	5	θ)(ϱσ−1	θ)(ϱσ−1	PROPN
ejpam-6138	182	6	)	)	PUNCT
ejpam-6138	182	7	(	(	PUNCT
ejpam-6138	182	8	ϱ−1	ϱ−1	PROPN
ejpam-6138	182	9	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	182	10	)	)	PUNCT
ejpam-6138	182	11	)	)	PUNCT
ejpam-6138	183	1	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	183	2	)	)	PUNCT
ejpam-6138	183	3	−	−	ADP
ejpam-6138	183	4	σ(ϑ	σ(ϑ	NOUN
ejpam-6138	183	5	−	−	NOUN
ejpam-6138	183	6	θ)ϱσ−1	θ)ϱσ−1	NOUN
ejpam-6138	183	7	(	(	PUNCT
ejpam-6138	183	8	ϱ−1	ϱ−1	PROPN
ejpam-6138	183	9	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	183	10	)	)	PUNCT
ejpam-6138	183	11	)	)	PUNCT
ejpam-6138	183	12	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	183	13	)	)	PUNCT
ejpam-6138	183	14	]	]	PUNCT
ejpam-6138	183	15	.	.	PUNCT
ejpam-6138	184	1	(	(	PUNCT
ejpam-6138	184	2	3.22	3.22	NUM
ejpam-6138	184	3	)	)	PUNCT
ejpam-6138	184	4	theorem	theorem	NOUN
ejpam-6138	184	5	4	4	NUM
ejpam-6138	184	6	(	(	PUNCT
ejpam-6138	184	7	[	[	X
ejpam-6138	184	8	17	17	NUM
ejpam-6138	184	9	]	]	NUM
ejpam-6138	184	10	)	)	PUNCT
ejpam-6138	184	11	.	.	PUNCT
ejpam-6138	185	1	assume	assume	VERB
ejpam-6138	185	2	ξ	ξ	X
ejpam-6138	186	1	∶	∶	X
ejpam-6138	186	2	[	[	X
ejpam-6138	186	3	θ	θ	X
ejpam-6138	186	4	,	,	PUNCT
ejpam-6138	186	5	ϑ	ϑ	X
ejpam-6138	186	6	]	]	X
ejpam-6138	186	7	×	×	NOUN
ejpam-6138	186	8	r2	r2	NOUN
ejpam-6138	186	9	→	→	PUNCT
ejpam-6138	186	10	r	r	NOUN
ejpam-6138	186	11	is	be	AUX
ejpam-6138	186	12	a	a	DET
ejpam-6138	186	13	function	function	NOUN
ejpam-6138	186	14	is	be	AUX
ejpam-6138	186	15	continuous	continuous	ADJ
ejpam-6138	186	16	and	and	CCONJ
ejpam-6138	186	17	check	check	VERB
ejpam-6138	186	18	a	a	DET
ejpam-6138	186	19	condition	condition	NOUN
ejpam-6138	186	20	of	of	ADP
ejpam-6138	186	21	uniform	uniform	ADJ
ejpam-6138	186	22	lipschitz	lipschitz	NOUN
ejpam-6138	186	23	concerning	concern	VERB
ejpam-6138	186	24	the	the	DET
ejpam-6138	186	25	second	second	ADJ
ejpam-6138	186	26	variable	variable	NOUN
ejpam-6138	186	27	on	on	ADP
ejpam-6138	186	28	[	[	X
ejpam-6138	186	29	θ	θ	NOUN
ejpam-6138	186	30	,	,	PUNCT
ejpam-6138	186	31	ϑ]×r2	ϑ]×r2	PROPN
ejpam-6138	186	32	with	with	ADP
ejpam-6138	186	33	lipschitz	lipschitz	VERB
ejpam-6138	186	34	real	real	ADJ
ejpam-6138	186	35	ζ	ζ	NOUN
ejpam-6138	186	36	,	,	PUNCT
ejpam-6138	186	37	thus	thus	ADV
ejpam-6138	186	38	,	,	PUNCT
ejpam-6138	186	39	»	»	PUNCT
ejpam-6138	186	40	»	»	PUNCT
ejpam-6138	186	41	»	»	PUNCT
ejpam-6138	186	42	»	»	PUNCT
ejpam-6138	186	43	»	»	PUNCT
ejpam-6138	186	44	»	»	X
ejpam-6138	186	45	ξ	ξ	X
ejpam-6138	186	46	(	(	PUNCT
ejpam-6138	186	47	τ	τ	PROPN
ejpam-6138	186	48	,	,	PUNCT
ejpam-6138	186	49	µ	µ	NOUN
ejpam-6138	186	50	,	,	PUNCT
ejpam-6138	186	51	µ′	µ′	NUM
ejpam-6138	186	52	)	)	PUNCT
ejpam-6138	186	53	−	−	PROPN
ejpam-6138	186	54	ξ	ξ	X
ejpam-6138	186	55	(	(	PUNCT
ejpam-6138	186	56	τ	τ	PROPN
ejpam-6138	186	57	,	,	PUNCT
ejpam-6138	186	58	ν	ν	PROPN
ejpam-6138	186	59	,	,	PUNCT
ejpam-6138	186	60	ν	ν	NOUN
ejpam-6138	186	61	′	′	NOUN
ejpam-6138	186	62	)	)	PUNCT
ejpam-6138	187	1	»	»	PRON
ejpam-6138	187	2	»	»	PUNCT
ejpam-6138	187	3	»	»	PUNCT
ejpam-6138	187	4	»	»	PRON
ejpam-6138	187	5	»	»	ADV
ejpam-6138	187	6	»	»	X
ejpam-6138	187	7	≤	≤	X
ejpam-6138	187	8	ζ∣µ	ζ∣µ	PUNCT
ejpam-6138	187	9	−	−	PROPN
ejpam-6138	187	10	ν∣	ν∣	NOUN
ejpam-6138	187	11	+	+	PUNCT
ejpam-6138	187	12	η∣µ′	η∣µ′	NOUN
ejpam-6138	187	13	−	−	NOUN
ejpam-6138	187	14	ν	ν	NOUN
ejpam-6138	187	15	′∣	′∣	PROPN
ejpam-6138	187	16	,	,	PUNCT
ejpam-6138	187	17	(	(	PUNCT
ejpam-6138	187	18	3.23	3.23	NUM
ejpam-6138	187	19	)	)	PUNCT
ejpam-6138	187	20	for	for	ADP
ejpam-6138	187	21	(	(	PUNCT
ejpam-6138	187	22	τ	τ	PROPN
ejpam-6138	187	23	,	,	PUNCT
ejpam-6138	187	24	µ	µ	NOUN
ejpam-6138	187	25	,	,	PUNCT
ejpam-6138	187	26	µ′	µ′	NOUN
ejpam-6138	187	27	)	)	PUNCT
ejpam-6138	187	28	,	,	PUNCT
ejpam-6138	187	29	(	(	PUNCT
ejpam-6138	187	30	τ	τ	X
ejpam-6138	187	31	,	,	PUNCT
ejpam-6138	187	32	ν	ν	PROPN
ejpam-6138	187	33	,	,	PUNCT
ejpam-6138	187	34	ν	ν	NOUN
ejpam-6138	187	35	′	′	NOUN
ejpam-6138	187	36	)	)	PUNCT
ejpam-6138	187	37	∈	∈	PROPN
ejpam-6138	187	38	[	[	X
ejpam-6138	187	39	θ	θ	X
ejpam-6138	187	40	,	,	PUNCT
ejpam-6138	187	41	ϑ	ϑ	X
ejpam-6138	187	42	]	]	X
ejpam-6138	187	43	×	×	NOUN
ejpam-6138	187	44	r2	r2	NOUN
ejpam-6138	187	45	,	,	PUNCT
ejpam-6138	187	46	where	where	SCONJ
ejpam-6138	187	47	η	η	PROPN
ejpam-6138	187	48	≥	≥	X
ejpam-6138	187	49	0	0	NUM
ejpam-6138	187	50	,	,	PUNCT
ejpam-6138	187	51	ζ	ζ	NOUN
ejpam-6138	187	52	>	>	SYM
ejpam-6138	187	53	0	0	NUM
ejpam-6138	187	54	are	be	AUX
ejpam-6138	187	55	constants	constant	NOUN
ejpam-6138	187	56	.	.	PUNCT
ejpam-6138	188	1	if	if	SCONJ
ejpam-6138	188	2	ζ	ζ	NOUN
ejpam-6138	188	3	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	188	4	)	)	PUNCT
ejpam-6138	188	5	[	[	PUNCT
ejpam-6138	188	6	(	(	PUNCT
ejpam-6138	188	7	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-6138	188	8	σ	σ	PROPN
ejpam-6138	188	9	1	1	PROPN
ejpam-6138	188	10	/	/	SYM
ejpam-6138	188	11	σ−1	σ−1	NUM
ejpam-6138	188	12	−	−	PROPN
ejpam-6138	188	13	(	(	PUNCT
ejpam-6138	188	14	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-6138	188	15	σ	σ	PROPN
ejpam-6138	188	16	σ	σ	PROPN
ejpam-6138	188	17	/	/	SYM
ejpam-6138	188	18	σ−1	σ−1	PROPN
ejpam-6138	188	19	]	]	PUNCT
ejpam-6138	189	1	+	+	CCONJ
ejpam-6138	189	2	η	η	PROPN
ejpam-6138	189	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	189	4	)	)	PUNCT
ejpam-6138	190	1	[	[	X
ejpam-6138	190	2	(	(	PUNCT
ejpam-6138	190	3	ϑ	ϑ	X
ejpam-6138	190	4	−	−	PROPN
ejpam-6138	190	5	θ)(ϱσ−1	θ)(ϱσ−1	PROPN
ejpam-6138	190	6	)	)	PUNCT
ejpam-6138	190	7	(	(	PUNCT
ejpam-6138	190	8	ϱ−1	ϱ−1	PROPN
ejpam-6138	190	9	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	190	10	)	)	PUNCT
ejpam-6138	190	11	)	)	PUNCT
ejpam-6138	191	1	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	191	2	)	)	PUNCT
ejpam-6138	191	3	−σ(ϑ	−σ(ϑ	ADP
ejpam-6138	191	4	−	−	PROPN
ejpam-6138	191	5	θ)ϱσ−1	θ)ϱσ−1	NOUN
ejpam-6138	191	6	(	(	PUNCT
ejpam-6138	191	7	ϱ−1	ϱ−1	PROPN
ejpam-6138	191	8	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	191	9	)	)	PUNCT
ejpam-6138	191	10	)	)	PUNCT
ejpam-6138	191	11	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	191	12	)	)	PUNCT
ejpam-6138	191	13	]	]	PUNCT
ejpam-6138	192	1	<	<	X
ejpam-6138	192	2	1	1	NUM
ejpam-6138	192	3	,	,	PUNCT
ejpam-6138	192	4	(	(	PUNCT
ejpam-6138	192	5	3.24	3.24	NUM
ejpam-6138	192	6	)	)	PUNCT
ejpam-6138	192	7	then	then	ADV
ejpam-6138	192	8	the	the	DET
ejpam-6138	192	9	bvp	bvp	PROPN
ejpam-6138	192	10	{	{	PUNCT
ejpam-6138	192	11	ϱ	ϱ	PROPN
ejpam-6138	192	12	cd	cd	PROPN
ejpam-6138	192	13	σ	σ	PROPN
ejpam-6138	192	14	0+µ(τ	0+µ(τ	PROPN
ejpam-6138	192	15	)	)	PUNCT
ejpam-6138	192	16	=	=	SYM
ejpam-6138	192	17	−ξ	−ξ	NOUN
ejpam-6138	192	18	(	(	PUNCT
ejpam-6138	192	19	τ	τ	PROPN
ejpam-6138	192	20	,	,	PUNCT
ejpam-6138	192	21	µ(τ	µ(τ	PROPN
ejpam-6138	192	22	)	)	PUNCT
ejpam-6138	192	23	,	,	PUNCT
ejpam-6138	192	24	ϱcdς	ϱcdς	ADJ
ejpam-6138	192	25	0+µ(τ	0+µ(τ	NOUN
ejpam-6138	192	26	)	)	PUNCT
ejpam-6138	192	27	)	)	PUNCT
ejpam-6138	192	28	,	,	PUNCT
ejpam-6138	192	29	0	0	PUNCT
ejpam-6138	192	30	<	<	X
ejpam-6138	192	31	τ	τ	X
ejpam-6138	192	32	<	<	X
ejpam-6138	192	33	1	1	NUM
ejpam-6138	192	34	,	,	PUNCT
ejpam-6138	192	35	µ(θ	µ(θ	ADJ
ejpam-6138	192	36	)	)	PUNCT
ejpam-6138	192	37	=	=	SYM
ejpam-6138	192	38	λ1	λ1	ADJ
ejpam-6138	192	39	,	,	PUNCT
ejpam-6138	192	40	µ(ϑ	µ(ϑ	PROPN
ejpam-6138	192	41	)	)	PUNCT
ejpam-6138	192	42	=	=	SYM
ejpam-6138	192	43	λ2	λ2	NOUN
ejpam-6138	192	44	,	,	PUNCT
ejpam-6138	192	45	(	(	PUNCT
ejpam-6138	192	46	3.25	3.25	NUM
ejpam-6138	192	47	)	)	PUNCT
ejpam-6138	192	48	has	have	VERB
ejpam-6138	192	49	a	a	DET
ejpam-6138	192	50	unique	unique	ADJ
ejpam-6138	192	51	solution	solution	NOUN
ejpam-6138	192	52	.	.	PUNCT
ejpam-6138	193	1	proof	proof	NOUN
ejpam-6138	193	2	.	.	PUNCT
ejpam-6138	194	1	using	use	VERB
ejpam-6138	194	2	the	the	DET
ejpam-6138	194	3	same	same	ADJ
ejpam-6138	194	4	method	method	NOUN
ejpam-6138	194	5	to	to	PART
ejpam-6138	194	6	prove	prove	VERB
ejpam-6138	194	7	proposition	proposition	NOUN
ejpam-6138	194	8	4	4	NUM
ejpam-6138	194	9	and	and	CCONJ
ejpam-6138	194	10	theorem	theorem	VERB
ejpam-6138	194	11	4	4	NUM
ejpam-6138	194	12	which	which	PRON
ejpam-6138	194	13	are	be	AUX
ejpam-6138	194	14	used	use	VERB
ejpam-6138	194	15	in	in	ADP
ejpam-6138	194	16	proposition	proposition	NOUN
ejpam-6138	194	17	2	2	NUM
ejpam-6138	194	18	and	and	CCONJ
ejpam-6138	194	19	also	also	ADV
ejpam-6138	194	20	applies	apply	VERB
ejpam-6138	194	21	to	to	PART
ejpam-6138	194	22	theorem	theorem	VERB
ejpam-6138	194	23	2	2	NUM
ejpam-6138	194	24	.	.	NOUN
ejpam-6138	194	25	remark	remark	NOUN
ejpam-6138	194	26	3	3	NUM
ejpam-6138	194	27	.	.	NOUN
ejpam-6138	194	28	same	same	ADJ
ejpam-6138	194	29	previous	previous	ADJ
ejpam-6138	194	30	notes	note	NOUN
ejpam-6138	194	31	.	.	PUNCT
ejpam-6138	195	1	we	we	PRON
ejpam-6138	195	2	notice	notice	VERB
ejpam-6138	195	3	them	they	PRON
ejpam-6138	195	4	in	in	ADP
ejpam-6138	195	5	the	the	DET
ejpam-6138	195	6	general	general	ADJ
ejpam-6138	195	7	case	case	NOUN
ejpam-6138	195	8	.	.	PUNCT
ejpam-6138	196	1	we	we	PRON
ejpam-6138	196	2	apply	apply	VERB
ejpam-6138	196	3	them	they	PRON
ejpam-6138	196	4	when	when	SCONJ
ejpam-6138	196	5	σ	σ	PROPN
ejpam-6138	196	6	=	=	SYM
ejpam-6138	196	7	2	2	NUM
ejpam-6138	196	8	,	,	PUNCT
ejpam-6138	196	9	θ	θ	PROPN
ejpam-6138	196	10	<	<	X
ejpam-6138	196	11	ϑ	ϑ	X
ejpam-6138	196	12	and	and	CCONJ
ejpam-6138	196	13	ϱ	ϱ	X
ejpam-6138	196	14	=	=	SYM
ejpam-6138	196	15	1	1	NUM
ejpam-6138	196	16	on	on	ADP
ejpam-6138	196	17	theorem	theorem	NOUN
ejpam-6138	196	18	4	4	NUM
ejpam-6138	196	19	,	,	PUNCT
ejpam-6138	196	20	through	through	ADP
ejpam-6138	196	21	condition	condition	NOUN
ejpam-6138	196	22	(	(	PUNCT
ejpam-6138	196	23	3.24	3.24	NUM
ejpam-6138	196	24	)	)	PUNCT
ejpam-6138	196	25	,	,	PUNCT
ejpam-6138	196	26	we	we	PRON
ejpam-6138	196	27	obviously	obviously	ADV
ejpam-6138	196	28	find	find	VERB
ejpam-6138	196	29	theorem	theorem	VERB
ejpam-6138	196	30	1	1	NUM
ejpam-6138	196	31	such	such	ADJ
ejpam-6138	196	32	that	that	SCONJ
ejpam-6138	196	33	ζ	ζ	PROPN
ejpam-6138	196	34	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	196	35	)	)	PUNCT
ejpam-6138	196	36	[	[	PUNCT
ejpam-6138	196	37	(	(	PUNCT
ejpam-6138	196	38	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-6138	196	39	σ	σ	PROPN
ejpam-6138	196	40	1	1	PROPN
ejpam-6138	196	41	/	/	SYM
ejpam-6138	196	42	σ−1	σ−1	NUM
ejpam-6138	196	43	−	−	PROPN
ejpam-6138	196	44	(	(	PUNCT
ejpam-6138	196	45	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-6138	196	46	σ	σ	PROPN
ejpam-6138	196	47	σ	σ	PROPN
ejpam-6138	196	48	/	/	SYM
ejpam-6138	196	49	σ−1	σ−1	PROPN
ejpam-6138	196	50	]	]	PUNCT
ejpam-6138	197	1	+	+	CCONJ
ejpam-6138	197	2	η	η	PROPN
ejpam-6138	197	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	197	4	)	)	PUNCT
ejpam-6138	198	1	[	[	X
ejpam-6138	198	2	(	(	PUNCT
ejpam-6138	198	3	ϑ	ϑ	X
ejpam-6138	198	4	−	−	PROPN
ejpam-6138	198	5	θ)(ϱσ−1	θ)(ϱσ−1	PROPN
ejpam-6138	198	6	)	)	PUNCT
ejpam-6138	198	7	(	(	PUNCT
ejpam-6138	198	8	ϱ−1	ϱ−1	PROPN
ejpam-6138	198	9	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	198	10	)	)	PUNCT
ejpam-6138	198	11	)	)	PUNCT
ejpam-6138	199	1	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	199	2	)	)	PUNCT
ejpam-6138	199	3	−σ(ϑ	−σ(ϑ	ADP
ejpam-6138	199	4	−	−	PROPN
ejpam-6138	199	5	θ)ϱσ−1	θ)ϱσ−1	NOUN
ejpam-6138	199	6	(	(	PUNCT
ejpam-6138	199	7	ϱ−1	ϱ−1	PROPN
ejpam-6138	199	8	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	199	9	)	)	PUNCT
ejpam-6138	199	10	)	)	PUNCT
ejpam-6138	199	11	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	199	12	)	)	PUNCT
ejpam-6138	199	13	]	]	PUNCT
ejpam-6138	200	1	=	=	PUNCT
ejpam-6138	200	2	ζ	ζ	X
ejpam-6138	200	3	(	(	PUNCT
ejpam-6138	200	4	ϑ−θ)2	ϑ−θ)2	NOUN
ejpam-6138	200	5	4γ(3	4γ(3	NUM
ejpam-6138	200	6	)	)	PUNCT
ejpam-6138	201	1	+	+	CCONJ
ejpam-6138	201	2	η	η	PROPN
ejpam-6138	201	3	(	(	PUNCT
ejpam-6138	201	4	ϑ−θ	ϑ−θ	NOUN
ejpam-6138	201	5	)	)	PUNCT
ejpam-6138	201	6	γ(3	γ(3	PROPN
ejpam-6138	201	7	)	)	PUNCT
ejpam-6138	201	8	<	<	X
ejpam-6138	201	9	1	1	X
ejpam-6138	201	10	.	.	PUNCT
ejpam-6138	201	11	proposition	proposition	NOUN
ejpam-6138	201	12	5	5	NUM
ejpam-6138	201	13	(	(	PUNCT
ejpam-6138	201	14	[	[	X
ejpam-6138	201	15	17	17	NUM
ejpam-6138	201	16	]	]	PUNCT
ejpam-6138	201	17	)	)	PUNCT
ejpam-6138	201	18	.	.	PUNCT
ejpam-6138	202	1	by	by	ADP
ejpam-6138	202	2	(	(	PUNCT
ejpam-6138	202	3	3.3	3.3	NUM
ejpam-6138	202	4	)	)	PUNCT
ejpam-6138	202	5	and	and	CCONJ
ejpam-6138	202	6	(	(	PUNCT
ejpam-6138	202	7	3.4	3.4	NUM
ejpam-6138	202	8	)	)	PUNCT
ejpam-6138	202	9	,	,	PUNCT
ejpam-6138	202	10	suppose	suppose	VERB
ejpam-6138	202	11	that	that	SCONJ
ejpam-6138	202	12	θ	θ	PROPN
ejpam-6138	202	13	<	<	X
ejpam-6138	202	14	ϑ	ϑ	X
ejpam-6138	202	15	=	=	SYM
ejpam-6138	202	16	1	1	NUM
ejpam-6138	202	17	then	then	ADV
ejpam-6138	202	18	∫	∫	PROPN
ejpam-6138	202	19	ϑ	ϑ	X
ejpam-6138	202	20	0	0	NUM
ejpam-6138	202	21	∣h̵(τ	∣h̵(τ	PROPN
ejpam-6138	202	22	,	,	PUNCT
ejpam-6138	202	23	r)∣dr	r)∣dr	X
ejpam-6138	202	24	≤	≤	ADV
ejpam-6138	202	25	1	1	NUM
ejpam-6138	202	26	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	202	27	)	)	PUNCT
ejpam-6138	202	28	[	[	PUNCT
ejpam-6138	202	29	(	(	PUNCT
ejpam-6138	202	30	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-6138	202	31	σ	σ	PROPN
ejpam-6138	202	32	1	1	NUM
ejpam-6138	202	33	/	/	SYM
ejpam-6138	202	34	σ−1	σ−1	NUM
ejpam-6138	202	35	−	−	PROPN
ejpam-6138	202	36	(	(	PUNCT
ejpam-6138	202	37	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-6138	202	38	σ	σ	PROPN
ejpam-6138	202	39	σ	σ	PROPN
ejpam-6138	202	40	/	/	SYM
ejpam-6138	202	41	σ−1	σ−1	PROPN
ejpam-6138	202	42	]	]	PUNCT
ejpam-6138	202	43	,	,	PUNCT
ejpam-6138	202	44	(	(	PUNCT
ejpam-6138	202	45	3.26	3.26	NUM
ejpam-6138	202	46	)	)	PUNCT
ejpam-6138	202	47	z.	z.	PROPN
ejpam-6138	202	48	bekri	bekri	PROPN
ejpam-6138	202	49	et	et	PROPN
ejpam-6138	202	50	al	al	PROPN
ejpam-6138	202	51	.	.	PUNCT
ejpam-6138	202	52	/	/	SYM
ejpam-6138	202	53	eur	eur	PROPN
ejpam-6138	202	54	.	.	PUNCT
ejpam-6138	203	1	j.	j.	PROPN
ejpam-6138	203	2	pure	pure	PROPN
ejpam-6138	203	3	appl	appl	PROPN
ejpam-6138	203	4	.	.	PROPN
ejpam-6138	203	5	math	math	PROPN
ejpam-6138	203	6	,	,	PUNCT
ejpam-6138	203	7	18	18	NUM
ejpam-6138	203	8	(	(	PUNCT
ejpam-6138	203	9	2	2	NUM
ejpam-6138	203	10	)	)	PUNCT
ejpam-6138	203	11	(	(	PUNCT
ejpam-6138	203	12	2025	2025	NUM
ejpam-6138	203	13	)	)	PUNCT
ejpam-6138	203	14	,	,	PUNCT
ejpam-6138	203	15	6138	6138	NUM
ejpam-6138	203	16	10	10	NUM
ejpam-6138	203	17	of	of	ADP
ejpam-6138	203	18	17	17	NUM
ejpam-6138	203	19	and	and	CCONJ
ejpam-6138	203	20	∫	∫	PROPN
ejpam-6138	203	21	ϑ	ϑ	X
ejpam-6138	203	22	0	0	NUM
ejpam-6138	203	23	∂∣h̵(τ	∂∣h̵(τ	PROPN
ejpam-6138	203	24	,	,	PUNCT
ejpam-6138	203	25	r)∣	r)∣	PROPN
ejpam-6138	203	26	∂τ	∂τ	PROPN
ejpam-6138	203	27	dr	dr	PROPN
ejpam-6138	203	28	≤	≤	PROPN
ejpam-6138	203	29	1	1	NUM
ejpam-6138	203	30	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	NOUN
ejpam-6138	203	31	)	)	PUNCT
ejpam-6138	204	1	[	[	X
ejpam-6138	204	2	(	(	PUNCT
ejpam-6138	204	3	1	1	NUM
ejpam-6138	204	4	−	−	PROPN
ejpam-6138	204	5	θ)(ϱσ−1	θ)(ϱσ−1	PROPN
ejpam-6138	204	6	)	)	PUNCT
ejpam-6138	204	7	(	(	PUNCT
ejpam-6138	204	8	ϱ−1	ϱ−1	PROPN
ejpam-6138	204	9	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	204	10	)	)	PUNCT
ejpam-6138	204	11	)	)	PUNCT
ejpam-6138	205	1	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	205	2	)	)	PUNCT
ejpam-6138	206	1	−	−	PROPN
ejpam-6138	206	2	σ(1	σ(1	PROPN
ejpam-6138	206	3	−	−	PROPN
ejpam-6138	206	4	θ)ϱσ−1	θ)ϱσ−1	NOUN
ejpam-6138	206	5	(	(	PUNCT
ejpam-6138	206	6	ϱ−1	ϱ−1	PROPN
ejpam-6138	206	7	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	206	8	)	)	PUNCT
ejpam-6138	206	9	)	)	PUNCT
ejpam-6138	206	10	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	206	11	)	)	PUNCT
ejpam-6138	206	12	]	]	PUNCT
ejpam-6138	206	13	.	.	PUNCT
ejpam-6138	207	1	(	(	PUNCT
ejpam-6138	207	2	3.27	3.27	NUM
ejpam-6138	207	3	)	)	PUNCT
ejpam-6138	207	4	theorem	theorem	NOUN
ejpam-6138	207	5	5	5	NUM
ejpam-6138	207	6	(	(	PUNCT
ejpam-6138	207	7	[	[	X
ejpam-6138	207	8	17	17	NUM
ejpam-6138	207	9	]	]	NUM
ejpam-6138	207	10	)	)	PUNCT
ejpam-6138	207	11	.	.	PUNCT
ejpam-6138	208	1	assume	assume	VERB
ejpam-6138	208	2	ξ	ξ	X
ejpam-6138	209	1	∶	∶	X
ejpam-6138	209	2	[	[	X
ejpam-6138	209	3	θ	θ	X
ejpam-6138	209	4	,	,	PUNCT
ejpam-6138	209	5	1	1	NUM
ejpam-6138	209	6	]	]	SYM
ejpam-6138	209	7	×	×	NOUN
ejpam-6138	209	8	r2	r2	NOUN
ejpam-6138	209	9	→	→	PUNCT
ejpam-6138	209	10	r	r	NOUN
ejpam-6138	209	11	is	be	AUX
ejpam-6138	209	12	a	a	DET
ejpam-6138	209	13	function	function	NOUN
ejpam-6138	209	14	is	be	AUX
ejpam-6138	209	15	continuous	continuous	ADJ
ejpam-6138	209	16	and	and	CCONJ
ejpam-6138	209	17	check	check	VERB
ejpam-6138	209	18	a	a	DET
ejpam-6138	209	19	condition	condition	NOUN
ejpam-6138	209	20	of	of	ADP
ejpam-6138	209	21	uniform	uniform	ADJ
ejpam-6138	209	22	lipschitz	lipschitz	NOUN
ejpam-6138	209	23	concerning	concern	VERB
ejpam-6138	209	24	the	the	DET
ejpam-6138	209	25	second	second	ADJ
ejpam-6138	209	26	variable	variable	NOUN
ejpam-6138	209	27	on	on	ADP
ejpam-6138	209	28	[	[	X
ejpam-6138	209	29	θ	θ	PROPN
ejpam-6138	209	30	,	,	PUNCT
ejpam-6138	209	31	1]×r2	1]×r2	NUM
ejpam-6138	209	32	with	with	ADP
ejpam-6138	209	33	lipschitz	lipschitz	VERB
ejpam-6138	209	34	real	real	ADJ
ejpam-6138	209	35	ζ	ζ	NOUN
ejpam-6138	209	36	,	,	PUNCT
ejpam-6138	209	37	thus	thus	ADV
ejpam-6138	209	38	,	,	PUNCT
ejpam-6138	209	39	»	»	PUNCT
ejpam-6138	209	40	»	»	PUNCT
ejpam-6138	209	41	»	»	PUNCT
ejpam-6138	209	42	»	»	PUNCT
ejpam-6138	209	43	»	»	PUNCT
ejpam-6138	209	44	»	»	X
ejpam-6138	209	45	ξ	ξ	X
ejpam-6138	209	46	(	(	PUNCT
ejpam-6138	209	47	τ	τ	PROPN
ejpam-6138	209	48	,	,	PUNCT
ejpam-6138	209	49	µ	µ	NOUN
ejpam-6138	209	50	,	,	PUNCT
ejpam-6138	209	51	µ′	µ′	NUM
ejpam-6138	209	52	)	)	PUNCT
ejpam-6138	209	53	−	−	PROPN
ejpam-6138	209	54	ξ	ξ	X
ejpam-6138	209	55	(	(	PUNCT
ejpam-6138	209	56	τ	τ	PROPN
ejpam-6138	209	57	,	,	PUNCT
ejpam-6138	209	58	ν	ν	PROPN
ejpam-6138	209	59	,	,	PUNCT
ejpam-6138	209	60	ν	ν	NOUN
ejpam-6138	209	61	′	′	NOUN
ejpam-6138	209	62	)	)	PUNCT
ejpam-6138	210	1	»	»	PRON
ejpam-6138	210	2	»	»	PUNCT
ejpam-6138	210	3	»	»	PUNCT
ejpam-6138	210	4	»	»	PRON
ejpam-6138	210	5	»	»	ADV
ejpam-6138	210	6	»	»	X
ejpam-6138	210	7	≤	≤	X
ejpam-6138	210	8	ζ∣µ	ζ∣µ	PUNCT
ejpam-6138	210	9	−	−	PROPN
ejpam-6138	210	10	ν∣	ν∣	NOUN
ejpam-6138	210	11	+	+	PUNCT
ejpam-6138	210	12	η∣µ′	η∣µ′	NOUN
ejpam-6138	210	13	−	−	NOUN
ejpam-6138	210	14	ν	ν	NOUN
ejpam-6138	210	15	′∣	′∣	PROPN
ejpam-6138	210	16	,	,	PUNCT
ejpam-6138	210	17	(	(	PUNCT
ejpam-6138	210	18	3.28	3.28	NUM
ejpam-6138	210	19	)	)	PUNCT
ejpam-6138	210	20	for	for	ADP
ejpam-6138	210	21	(	(	PUNCT
ejpam-6138	210	22	τ	τ	PROPN
ejpam-6138	210	23	,	,	PUNCT
ejpam-6138	210	24	µ	µ	NOUN
ejpam-6138	210	25	,	,	PUNCT
ejpam-6138	210	26	µ′	µ′	NOUN
ejpam-6138	210	27	)	)	PUNCT
ejpam-6138	210	28	,	,	PUNCT
ejpam-6138	210	29	(	(	PUNCT
ejpam-6138	210	30	τ	τ	X
ejpam-6138	210	31	,	,	PUNCT
ejpam-6138	210	32	ν	ν	PROPN
ejpam-6138	210	33	,	,	PUNCT
ejpam-6138	210	34	ν	ν	NOUN
ejpam-6138	210	35	′	′	NOUN
ejpam-6138	210	36	)	)	PUNCT
ejpam-6138	210	37	∈	∈	PROPN
ejpam-6138	210	38	[	[	X
ejpam-6138	210	39	θ	θ	X
ejpam-6138	210	40	,	,	PUNCT
ejpam-6138	210	41	1	1	NUM
ejpam-6138	210	42	]	]	SYM
ejpam-6138	210	43	×	×	NOUN
ejpam-6138	210	44	r2	r2	NOUN
ejpam-6138	210	45	,	,	PUNCT
ejpam-6138	210	46	where	where	SCONJ
ejpam-6138	210	47	η	η	PROPN
ejpam-6138	210	48	≥	≥	X
ejpam-6138	210	49	0	0	NUM
ejpam-6138	210	50	,	,	PUNCT
ejpam-6138	210	51	ζ	ζ	NOUN
ejpam-6138	210	52	>	>	SYM
ejpam-6138	210	53	0	0	NUM
ejpam-6138	210	54	are	be	AUX
ejpam-6138	210	55	constants	constant	NOUN
ejpam-6138	210	56	.	.	PUNCT
ejpam-6138	211	1	if	if	SCONJ
ejpam-6138	211	2	ζ	ζ	NOUN
ejpam-6138	211	3	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	211	4	)	)	PUNCT
ejpam-6138	211	5	[	[	PUNCT
ejpam-6138	211	6	(	(	PUNCT
ejpam-6138	211	7	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-6138	211	8	σ	σ	PROPN
ejpam-6138	211	9	1	1	NUM
ejpam-6138	211	10	/	/	SYM
ejpam-6138	212	1	σ−1	σ−1	NUM
ejpam-6138	212	2	−	−	PROPN
ejpam-6138	213	1	(	(	PUNCT
ejpam-6138	213	2	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-6138	213	3	σ	σ	PROPN
ejpam-6138	213	4	σ	σ	PROPN
ejpam-6138	213	5	/	/	SYM
ejpam-6138	213	6	σ−1	σ−1	PROPN
ejpam-6138	213	7	]	]	PUNCT
ejpam-6138	214	1	+	+	CCONJ
ejpam-6138	214	2	η	η	PROPN
ejpam-6138	214	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	214	4	)	)	PUNCT
ejpam-6138	215	1	[	[	X
ejpam-6138	215	2	(	(	PUNCT
ejpam-6138	215	3	1	1	NUM
ejpam-6138	215	4	−	−	PROPN
ejpam-6138	215	5	θ)(ϱσ−1	θ)(ϱσ−1	PROPN
ejpam-6138	215	6	)	)	PUNCT
ejpam-6138	215	7	(	(	PUNCT
ejpam-6138	215	8	ϱ−1	ϱ−1	PROPN
ejpam-6138	215	9	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	215	10	)	)	PUNCT
ejpam-6138	215	11	)	)	PUNCT
ejpam-6138	216	1	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	216	2	)	)	PUNCT
ejpam-6138	217	1	−σ(1	−σ(1	PROPN
ejpam-6138	217	2	−	−	PROPN
ejpam-6138	217	3	θ)ϱσ−1	θ)ϱσ−1	VERB
ejpam-6138	217	4	(	(	PUNCT
ejpam-6138	217	5	ϱ−1	ϱ−1	PROPN
ejpam-6138	217	6	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	217	7	)	)	PUNCT
ejpam-6138	217	8	)	)	PUNCT
ejpam-6138	217	9	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	217	10	)	)	PUNCT
ejpam-6138	217	11	]	]	PUNCT
ejpam-6138	217	12	<	<	X
ejpam-6138	217	13	1	1	NUM
ejpam-6138	217	14	,	,	PUNCT
ejpam-6138	217	15	(	(	PUNCT
ejpam-6138	217	16	3.29	3.29	NUM
ejpam-6138	217	17	)	)	PUNCT
ejpam-6138	217	18	then	then	ADV
ejpam-6138	217	19	the	the	DET
ejpam-6138	217	20	bvp	bvp	PROPN
ejpam-6138	217	21	{	{	PUNCT
ejpam-6138	217	22	ϱ	ϱ	PROPN
ejpam-6138	217	23	cd	cd	PROPN
ejpam-6138	217	24	σ	σ	PROPN
ejpam-6138	217	25	0+µ(τ	0+µ(τ	PROPN
ejpam-6138	217	26	)	)	PUNCT
ejpam-6138	217	27	=	=	SYM
ejpam-6138	217	28	−ξ	−ξ	NOUN
ejpam-6138	217	29	(	(	PUNCT
ejpam-6138	217	30	τ	τ	PROPN
ejpam-6138	217	31	,	,	PUNCT
ejpam-6138	217	32	µ(τ	µ(τ	PROPN
ejpam-6138	217	33	)	)	PUNCT
ejpam-6138	217	34	,	,	PUNCT
ejpam-6138	217	35	ϱcdς	ϱcdς	ADJ
ejpam-6138	217	36	0+µ(τ	0+µ(τ	NOUN
ejpam-6138	217	37	)	)	PUNCT
ejpam-6138	217	38	)	)	PUNCT
ejpam-6138	217	39	,	,	PUNCT
ejpam-6138	217	40	0	0	PUNCT
ejpam-6138	217	41	<	<	X
ejpam-6138	217	42	τ	τ	X
ejpam-6138	217	43	<	<	X
ejpam-6138	217	44	1	1	NUM
ejpam-6138	217	45	,	,	PUNCT
ejpam-6138	217	46	µ(θ	µ(θ	ADJ
ejpam-6138	217	47	)	)	PUNCT
ejpam-6138	217	48	=	=	SYM
ejpam-6138	217	49	λ1	λ1	PROPN
ejpam-6138	217	50	,	,	PUNCT
ejpam-6138	217	51	µ(1	µ(1	PROPN
ejpam-6138	217	52	)	)	PUNCT
ejpam-6138	217	53	=	=	SYM
ejpam-6138	217	54	λ2	λ2	PROPN
ejpam-6138	217	55	,	,	PUNCT
ejpam-6138	217	56	(	(	PUNCT
ejpam-6138	217	57	3.30	3.30	NUM
ejpam-6138	217	58	)	)	PUNCT
ejpam-6138	217	59	has	have	VERB
ejpam-6138	217	60	a	a	DET
ejpam-6138	217	61	unique	unique	ADJ
ejpam-6138	217	62	solution	solution	NOUN
ejpam-6138	217	63	.	.	PUNCT
ejpam-6138	218	1	proof	proof	NOUN
ejpam-6138	218	2	.	.	PUNCT
ejpam-6138	219	1	using	use	VERB
ejpam-6138	219	2	the	the	DET
ejpam-6138	219	3	same	same	ADJ
ejpam-6138	219	4	method	method	NOUN
ejpam-6138	219	5	to	to	PART
ejpam-6138	219	6	prove	prove	VERB
ejpam-6138	219	7	proposition	proposition	NOUN
ejpam-6138	219	8	5	5	NUM
ejpam-6138	219	9	and	and	CCONJ
ejpam-6138	219	10	theorem	theorem	VERB
ejpam-6138	219	11	5	5	NUM
ejpam-6138	219	12	which	which	PRON
ejpam-6138	219	13	are	be	AUX
ejpam-6138	219	14	used	use	VERB
ejpam-6138	219	15	in	in	ADP
ejpam-6138	219	16	proposition	proposition	NOUN
ejpam-6138	219	17	2	2	NUM
ejpam-6138	219	18	and	and	CCONJ
ejpam-6138	219	19	also	also	ADV
ejpam-6138	219	20	applies	apply	VERB
ejpam-6138	219	21	to	to	PART
ejpam-6138	219	22	theorem	theorem	VERB
ejpam-6138	219	23	2	2	NUM
ejpam-6138	219	24	.	.	NOUN
ejpam-6138	219	25	remark	remark	NOUN
ejpam-6138	219	26	4	4	NUM
ejpam-6138	219	27	.	.	NOUN
ejpam-6138	219	28	same	same	ADJ
ejpam-6138	219	29	previous	previous	ADJ
ejpam-6138	219	30	notes	note	NOUN
ejpam-6138	219	31	.	.	PUNCT
ejpam-6138	220	1	we	we	PRON
ejpam-6138	220	2	notice	notice	VERB
ejpam-6138	220	3	them	they	PRON
ejpam-6138	220	4	in	in	ADP
ejpam-6138	220	5	the	the	DET
ejpam-6138	220	6	general	general	ADJ
ejpam-6138	220	7	case	case	NOUN
ejpam-6138	220	8	.	.	PUNCT
ejpam-6138	221	1	we	we	PRON
ejpam-6138	221	2	apply	apply	VERB
ejpam-6138	221	3	them	they	PRON
ejpam-6138	221	4	when	when	SCONJ
ejpam-6138	221	5	σ	σ	PROPN
ejpam-6138	221	6	=	=	SYM
ejpam-6138	221	7	2	2	NUM
ejpam-6138	221	8	,	,	PUNCT
ejpam-6138	221	9	θ	θ	X
ejpam-6138	221	10	<	<	X
ejpam-6138	221	11	ϑ	ϑ	X
ejpam-6138	221	12	=	=	SYM
ejpam-6138	221	13	1	1	NUM
ejpam-6138	221	14	and	and	CCONJ
ejpam-6138	221	15	ϱ	ϱ	X
ejpam-6138	221	16	=	=	SYM
ejpam-6138	221	17	1	1	NUM
ejpam-6138	221	18	on	on	ADP
ejpam-6138	221	19	theorem	theorem	NOUN
ejpam-6138	221	20	5	5	NUM
ejpam-6138	221	21	,	,	PUNCT
ejpam-6138	221	22	through	through	ADP
ejpam-6138	221	23	condition	condition	NOUN
ejpam-6138	221	24	(	(	PUNCT
ejpam-6138	221	25	3.29	3.29	NUM
ejpam-6138	221	26	)	)	PUNCT
ejpam-6138	221	27	,	,	PUNCT
ejpam-6138	221	28	we	we	PRON
ejpam-6138	221	29	obviously	obviously	ADV
ejpam-6138	221	30	find	find	VERB
ejpam-6138	221	31	theorem	theorem	VERB
ejpam-6138	221	32	1	1	NUM
ejpam-6138	221	33	such	such	ADJ
ejpam-6138	221	34	that	that	SCONJ
ejpam-6138	221	35	ζ	ζ	PROPN
ejpam-6138	221	36	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	221	37	)	)	PUNCT
ejpam-6138	221	38	[	[	PUNCT
ejpam-6138	221	39	(	(	PUNCT
ejpam-6138	221	40	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-6138	221	41	σ	σ	PROPN
ejpam-6138	221	42	1	1	NUM
ejpam-6138	221	43	/	/	SYM
ejpam-6138	222	1	σ−1	σ−1	NUM
ejpam-6138	222	2	−	−	PROPN
ejpam-6138	223	1	(	(	PUNCT
ejpam-6138	223	2	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-6138	223	3	σ	σ	PROPN
ejpam-6138	223	4	σ	σ	PROPN
ejpam-6138	223	5	/	/	SYM
ejpam-6138	223	6	σ−1	σ−1	PROPN
ejpam-6138	223	7	]	]	PUNCT
ejpam-6138	224	1	+	+	CCONJ
ejpam-6138	224	2	η	η	PROPN
ejpam-6138	224	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	224	4	)	)	PUNCT
ejpam-6138	225	1	[	[	X
ejpam-6138	225	2	(	(	PUNCT
ejpam-6138	225	3	1	1	NUM
ejpam-6138	225	4	−	−	PROPN
ejpam-6138	225	5	θ)(ϱσ−1	θ)(ϱσ−1	PROPN
ejpam-6138	225	6	)	)	PUNCT
ejpam-6138	225	7	(	(	PUNCT
ejpam-6138	225	8	ϱ−1	ϱ−1	PROPN
ejpam-6138	225	9	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	225	10	)	)	PUNCT
ejpam-6138	225	11	)	)	PUNCT
ejpam-6138	226	1	ϱ−1/ϱ(σ−1	ϱ−1/ϱ(σ−1	X
ejpam-6138	226	2	)	)	PUNCT
ejpam-6138	227	1	−σ(1	−σ(1	PROPN
ejpam-6138	227	2	−	−	PROPN
ejpam-6138	227	3	θ)ϱσ−1	θ)ϱσ−1	VERB
ejpam-6138	227	4	(	(	PUNCT
ejpam-6138	227	5	ϱ−1	ϱ−1	PROPN
ejpam-6138	227	6	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	227	7	)	)	PUNCT
ejpam-6138	227	8	)	)	PUNCT
ejpam-6138	227	9	ϱσ−1/ϱ(σ−1	ϱσ−1/ϱ(σ−1	PROPN
ejpam-6138	227	10	)	)	PUNCT
ejpam-6138	227	11	]	]	PUNCT
ejpam-6138	228	1	=	=	PUNCT
ejpam-6138	228	2	ζ	ζ	X
ejpam-6138	228	3	(	(	PUNCT
ejpam-6138	228	4	1−θ)2	1−θ)2	NUM
ejpam-6138	228	5	4γ(3	4γ(3	NUM
ejpam-6138	228	6	)	)	PUNCT
ejpam-6138	229	1	+	+	CCONJ
ejpam-6138	229	2	η	η	PROPN
ejpam-6138	229	3	(	(	PUNCT
ejpam-6138	229	4	1−θ	1−θ	NUM
ejpam-6138	229	5	)	)	PUNCT
ejpam-6138	229	6	γ(3	γ(3	PROPN
ejpam-6138	229	7	)	)	PUNCT
ejpam-6138	229	8	<	<	X
ejpam-6138	229	9	1	1	NUM
ejpam-6138	229	10	.	.	SYM
ejpam-6138	229	11	4	4	NUM
ejpam-6138	229	12	.	.	X
ejpam-6138	229	13	applications	application	NOUN
ejpam-6138	229	14	to	to	PART
ejpam-6138	229	15	prove	prove	VERB
ejpam-6138	229	16	the	the	DET
ejpam-6138	229	17	desired	desire	VERB
ejpam-6138	229	18	results	result	NOUN
ejpam-6138	229	19	above	above	ADV
ejpam-6138	229	20	,	,	PUNCT
ejpam-6138	229	21	we	we	PRON
ejpam-6138	229	22	take	take	VERB
ejpam-6138	229	23	some	some	DET
ejpam-6138	229	24	applications	application	NOUN
ejpam-6138	229	25	.	.	PUNCT
ejpam-6138	230	1	example	example	NOUN
ejpam-6138	231	1	1	1	NUM
ejpam-6138	231	2	.	.	X
ejpam-6138	231	3	extrapolate	extrapolate	VERB
ejpam-6138	231	4	the	the	DET
ejpam-6138	231	5	following	follow	VERB
ejpam-6138	231	6	application	application	NOUN
ejpam-6138	231	7	of	of	ADP
ejpam-6138	231	8	bvp	bvp	PROPN
ejpam-6138	231	9	{	{	PUNCT
ejpam-6138	231	10	1	1	NUM
ejpam-6138	231	11	cd	cd	PROPN
ejpam-6138	231	12	σ	σ	PROPN
ejpam-6138	231	13	0+µ(τ	0+µ(τ	PROPN
ejpam-6138	231	14	)	)	PUNCT
ejpam-6138	231	15	=	=	NOUN
ejpam-6138	231	16	7	7	NUM
ejpam-6138	231	17	−	−	NOUN
ejpam-6138	231	18	τ	τ	PROPN
ejpam-6138	231	19	5	5	NUM
ejpam-6138	231	20	−	−	PROPN
ejpam-6138	231	21	sin(µ(τ	sin(µ(τ	NOUN
ejpam-6138	231	22	)	)	PUNCT
ejpam-6138	231	23	)	)	PUNCT
ejpam-6138	232	1	−	−	PROPN
ejpam-6138	232	2	1	1	NUM
ejpam-6138	232	3	cd	cd	NOUN
ejpam-6138	232	4	1	1	NUM
ejpam-6138	232	5	0	0	NUM
ejpam-6138	232	6	+	+	NUM
ejpam-6138	232	7	cos(µ(τ	cos(µ(τ	NOUN
ejpam-6138	232	8	)	)	PUNCT
ejpam-6138	232	9	)	)	PUNCT
ejpam-6138	232	10	,	,	PUNCT
ejpam-6138	232	11	0	0	PUNCT
ejpam-6138	232	12	<	<	X
ejpam-6138	232	13	τ	τ	X
ejpam-6138	232	14	<	<	X
ejpam-6138	232	15	ϑ	ϑ	X
ejpam-6138	232	16	,	,	PUNCT
ejpam-6138	232	17	µ(0	µ(0	NOUN
ejpam-6138	232	18	)	)	PUNCT
ejpam-6138	232	19	=	=	SYM
ejpam-6138	232	20	2	2	NUM
ejpam-6138	232	21	,	,	PUNCT
ejpam-6138	232	22	µ(ϑ	µ(ϑ	NOUN
ejpam-6138	232	23	)	)	PUNCT
ejpam-6138	232	24	=	=	SYM
ejpam-6138	233	1	3	3	X
ejpam-6138	233	2	.	.	PUNCT
ejpam-6138	233	3	(	(	PUNCT
ejpam-6138	233	4	4.1	4.1	NUM
ejpam-6138	233	5	)	)	PUNCT
ejpam-6138	233	6	z.	z.	PROPN
ejpam-6138	233	7	bekri	bekri	PROPN
ejpam-6138	233	8	et	et	PROPN
ejpam-6138	233	9	al	al	PROPN
ejpam-6138	233	10	.	.	PUNCT
ejpam-6138	233	11	/	/	SYM
ejpam-6138	233	12	eur	eur	PROPN
ejpam-6138	233	13	.	.	PUNCT
ejpam-6138	234	1	j.	j.	PROPN
ejpam-6138	234	2	pure	pure	PROPN
ejpam-6138	234	3	appl	appl	PROPN
ejpam-6138	234	4	.	.	PROPN
ejpam-6138	234	5	math	math	PROPN
ejpam-6138	234	6	,	,	PUNCT
ejpam-6138	234	7	18	18	NUM
ejpam-6138	234	8	(	(	PUNCT
ejpam-6138	234	9	2	2	NUM
ejpam-6138	234	10	)	)	PUNCT
ejpam-6138	234	11	(	(	PUNCT
ejpam-6138	234	12	2025	2025	NUM
ejpam-6138	234	13	)	)	PUNCT
ejpam-6138	234	14	,	,	PUNCT
ejpam-6138	234	15	6138	6138	NUM
ejpam-6138	234	16	11	11	NUM
ejpam-6138	234	17	of	of	ADP
ejpam-6138	234	18	17	17	NUM
ejpam-6138	234	19	set	set	NOUN
ejpam-6138	234	20	,	,	PUNCT
ejpam-6138	234	21	ϱ	ϱ	X
ejpam-6138	234	22	=	=	SYM
ejpam-6138	234	23	1	1	NUM
ejpam-6138	234	24	,	,	PUNCT
ejpam-6138	234	25	σ	σ	NOUN
ejpam-6138	234	26	=	=	PUNCT
ejpam-6138	234	27	{	{	PUNCT
ejpam-6138	234	28	1.5	1.5	NUM
ejpam-6138	234	29	,	,	PUNCT
ejpam-6138	234	30	1.65	1.65	NUM
ejpam-6138	234	31	,	,	PUNCT
ejpam-6138	234	32	1.8	1.8	NUM
ejpam-6138	234	33	,	,	PUNCT
ejpam-6138	234	34	1.95	1.95	NUM
ejpam-6138	234	35	}	}	PUNCT
ejpam-6138	234	36	,	,	PUNCT
ejpam-6138	234	37	ς	ς	PROPN
ejpam-6138	234	38	=	=	SYM
ejpam-6138	234	39	1	1	NUM
ejpam-6138	234	40	,	,	PUNCT
ejpam-6138	234	41	θ	θ	PROPN
ejpam-6138	234	42	=	=	SYM
ejpam-6138	234	43	0	0	NUM
ejpam-6138	234	44	and	and	CCONJ
ejpam-6138	234	45	ξ	ξ	X
ejpam-6138	234	46	(	(	PUNCT
ejpam-6138	234	47	τ	τ	PROPN
ejpam-6138	234	48	,	,	PUNCT
ejpam-6138	234	49	µ(τ	µ(τ	PROPN
ejpam-6138	234	50	)	)	PUNCT
ejpam-6138	234	51	,	,	PUNCT
ejpam-6138	234	52	ϱcdς	ϱcdς	ADJ
ejpam-6138	234	53	θ+µ(τ	θ+µ(τ	NOUN
ejpam-6138	234	54	)	)	PUNCT
ejpam-6138	234	55	)	)	PUNCT
ejpam-6138	235	1	=	=	PUNCT
ejpam-6138	235	2	τ	τ	X
ejpam-6138	235	3	5	5	NUM
ejpam-6138	235	4	−	−	PROPN
ejpam-6138	235	5	7	7	NUM
ejpam-6138	235	6	+	+	NUM
ejpam-6138	235	7	sin(µ(τ	sin(µ(τ	NOUN
ejpam-6138	235	8	)	)	PUNCT
ejpam-6138	235	9	)	)	PUNCT
ejpam-6138	236	1	+	+	CCONJ
ejpam-6138	236	2	1	1	NUM
ejpam-6138	236	3	cd	cd	NOUN
ejpam-6138	236	4	1	1	NUM
ejpam-6138	236	5	0	0	NUM
ejpam-6138	236	6	+	+	NUM
ejpam-6138	236	7	cos(µ(τ	cos(µ(τ	NOUN
ejpam-6138	236	8	)	)	PUNCT
ejpam-6138	236	9	)	)	PUNCT
ejpam-6138	236	10	.	.	PUNCT
ejpam-6138	237	1	here	here	ADV
ejpam-6138	237	2	,	,	PUNCT
ejpam-6138	237	3	»	»	PUNCT
ejpam-6138	237	4	»	»	PUNCT
ejpam-6138	237	5	»	»	PRON
ejpam-6138	237	6	»	»	PUNCT
ejpam-6138	237	7	»	»	PUNCT
ejpam-6138	237	8	»	»	X
ejpam-6138	237	9	ξ	ξ	X
ejpam-6138	237	10	(	(	PUNCT
ejpam-6138	237	11	τ	τ	PROPN
ejpam-6138	237	12	,	,	PUNCT
ejpam-6138	237	13	µ	µ	NOUN
ejpam-6138	237	14	,	,	PUNCT
ejpam-6138	237	15	µ′	µ′	NUM
ejpam-6138	237	16	)	)	PUNCT
ejpam-6138	237	17	−	−	PROPN
ejpam-6138	237	18	ξ	ξ	X
ejpam-6138	237	19	(	(	PUNCT
ejpam-6138	237	20	τ	τ	PROPN
ejpam-6138	237	21	,	,	PUNCT
ejpam-6138	237	22	ν	ν	PROPN
ejpam-6138	237	23	,	,	PUNCT
ejpam-6138	237	24	ν	ν	NOUN
ejpam-6138	237	25	′	′	NOUN
ejpam-6138	237	26	)	)	PUNCT
ejpam-6138	237	27	»	»	PRON
ejpam-6138	237	28	»	»	PUNCT
ejpam-6138	237	29	»	»	PUNCT
ejpam-6138	237	30	»	»	PRON
ejpam-6138	237	31	»	»	PUNCT
ejpam-6138	237	32	»	»	PUNCT
ejpam-6138	237	33	=	=	NOUN
ejpam-6138	237	34	»	»	X
ejpam-6138	237	35	»	»	PUNCT
ejpam-6138	237	36	»	»	PUNCT
ejpam-6138	237	37	»	»	PUNCT
ejpam-6138	237	38	»	»	PUNCT
ejpam-6138	237	39	»	»	X
ejpam-6138	237	40	τ	τ	X
ejpam-6138	237	41	5	5	NUM
ejpam-6138	237	42	−	−	NOUN
ejpam-6138	237	43	7	7	NUM
ejpam-6138	237	44	+	+	NUM
ejpam-6138	237	45	sin(µ	sin(µ	NOUN
ejpam-6138	237	46	)	)	PUNCT
ejpam-6138	237	47	+	+	NUM
ejpam-6138	237	48	cos(µ′	cos(µ′	PROPN
ejpam-6138	237	49	)	)	PUNCT
ejpam-6138	238	1	−	−	PROPN
ejpam-6138	239	1	(	(	PUNCT
ejpam-6138	239	2	τ5	τ5	NOUN
ejpam-6138	239	3	−	−	PROPN
ejpam-6138	239	4	7	7	NUM
ejpam-6138	239	5	+	+	NUM
ejpam-6138	239	6	sin(ν	sin(ν	NOUN
ejpam-6138	239	7	)	)	PUNCT
ejpam-6138	240	1	+	+	SYM
ejpam-6138	240	2	cos(ν	cos(ν	NUM
ejpam-6138	240	3	′	′	NUM
ejpam-6138	240	4	)	)	PUNCT
ejpam-6138	240	5	)	)	PUNCT
ejpam-6138	241	1	»	»	PUNCT
ejpam-6138	241	2	»	»	PUNCT
ejpam-6138	241	3	»	»	PUNCT
ejpam-6138	241	4	»	»	PRON
ejpam-6138	241	5	»	»	ADV
ejpam-6138	241	6	»	»	X
ejpam-6138	241	7	≤	≤	NOUN
ejpam-6138	241	8	»	»	PUNCT
ejpam-6138	241	9	»	»	PUNCT
ejpam-6138	241	10	»	»	PRON
ejpam-6138	241	11	»	»	PRON
ejpam-6138	241	12	»	»	PRON
ejpam-6138	241	13	»	»	X
ejpam-6138	241	14	sin(µ	sin(µ	PROPN
ejpam-6138	241	15	)	)	PUNCT
ejpam-6138	241	16	−	−	PROPN
ejpam-6138	241	17	sin(ν	sin(ν	NOUN
ejpam-6138	241	18	)	)	PUNCT
ejpam-6138	241	19	»	»	PUNCT
ejpam-6138	241	20	»	»	PUNCT
ejpam-6138	241	21	»	»	PUNCT
ejpam-6138	241	22	»	»	PRON
ejpam-6138	241	23	»	»	PRON
ejpam-6138	241	24	»	»	PUNCT
ejpam-6138	241	25	+	+	ADJ
ejpam-6138	241	26	»	»	PUNCT
ejpam-6138	241	27	»	»	PRON
ejpam-6138	241	28	»	»	PUNCT
ejpam-6138	241	29	»	»	PRON
ejpam-6138	241	30	»	»	PUNCT
ejpam-6138	241	31	»	»	PUNCT
ejpam-6138	241	32	cos(µ	cos(µ	PROPN
ejpam-6138	241	33	′	′	PROPN
ejpam-6138	241	34	)	)	PUNCT
ejpam-6138	241	35	−	−	PROPN
ejpam-6138	241	36	cos(ν	cos(ν	PROPN
ejpam-6138	241	37	′	′	NOUN
ejpam-6138	241	38	)	)	PUNCT
ejpam-6138	241	39	»	»	PUNCT
ejpam-6138	241	40	»	»	PUNCT
ejpam-6138	241	41	»	»	PUNCT
ejpam-6138	241	42	»	»	PRON
ejpam-6138	241	43	»	»	ADV
ejpam-6138	241	44	»	»	X
ejpam-6138	241	45	≤	≤	ADV
ejpam-6138	242	1	∣µ	∣µ	NUM
ejpam-6138	242	2	−	−	PROPN
ejpam-6138	242	3	ν∣	ν∣	NOUN
ejpam-6138	242	4	+	+	CCONJ
ejpam-6138	242	5	»	»	PUNCT
ejpam-6138	242	6	»	»	PRON
ejpam-6138	242	7	»	»	PRON
ejpam-6138	242	8	»	»	PUNCT
ejpam-6138	242	9	»	»	PUNCT
ejpam-6138	242	10	»	»	PUNCT
ejpam-6138	242	11	−2	−2	PROPN
ejpam-6138	242	12	sin	sin	NOUN
ejpam-6138	242	13	µ	µ	PROPN
ejpam-6138	242	14	′+ν	′+ν	NUM
ejpam-6138	242	15	′	′	NUM
ejpam-6138	242	16	2	2	NUM
ejpam-6138	242	17	sin	sin	NOUN
ejpam-6138	242	18	µ	µ	X
ejpam-6138	242	19	′−ν	′−ν	NOUN
ejpam-6138	242	20	′	′	NUM
ejpam-6138	242	21	2	2	NUM
ejpam-6138	242	22	»	»	NOUN
ejpam-6138	242	23	»	»	PUNCT
ejpam-6138	242	24	»	»	PRON
ejpam-6138	242	25	»	»	PRON
ejpam-6138	242	26	»	»	ADV
ejpam-6138	242	27	»	»	X
ejpam-6138	242	28	≤	≤	X
ejpam-6138	242	29	ζ∣µ	ζ∣µ	PUNCT
ejpam-6138	242	30	−	−	PROPN
ejpam-6138	242	31	ν∣	ν∣	NOUN
ejpam-6138	242	32	+	+	PUNCT
ejpam-6138	242	33	η∣µ′	η∣µ′	NOUN
ejpam-6138	242	34	−	−	NOUN
ejpam-6138	242	35	ν	ν	NOUN
ejpam-6138	242	36	′∣	′∣	PROPN
ejpam-6138	242	37	,	,	PUNCT
ejpam-6138	242	38	for	for	ADP
ejpam-6138	242	39	(	(	PUNCT
ejpam-6138	242	40	τ	τ	PROPN
ejpam-6138	242	41	,	,	PUNCT
ejpam-6138	242	42	µ	µ	NOUN
ejpam-6138	242	43	,	,	PUNCT
ejpam-6138	242	44	µ′	µ′	NOUN
ejpam-6138	242	45	)	)	PUNCT
ejpam-6138	242	46	,	,	PUNCT
ejpam-6138	242	47	(	(	PUNCT
ejpam-6138	242	48	τ	τ	X
ejpam-6138	242	49	,	,	PUNCT
ejpam-6138	242	50	ν	ν	PROPN
ejpam-6138	242	51	,	,	PUNCT
ejpam-6138	242	52	ν	ν	NOUN
ejpam-6138	242	53	′	′	NOUN
ejpam-6138	242	54	)	)	PUNCT
ejpam-6138	242	55	∈	∈	PROPN
ejpam-6138	243	1	[	[	X
ejpam-6138	243	2	0	0	NUM
ejpam-6138	243	3	,	,	PUNCT
ejpam-6138	243	4	ϑ	ϑ	X
ejpam-6138	243	5	]	]	X
ejpam-6138	243	6	×	×	NOUN
ejpam-6138	243	7	r2	r2	NOUN
ejpam-6138	243	8	,	,	PUNCT
ejpam-6138	243	9	where	where	SCONJ
ejpam-6138	243	10	η	η	PROPN
ejpam-6138	243	11	=	=	PROPN
ejpam-6138	243	12	1	1	NUM
ejpam-6138	243	13	≥	≥	NOUN
ejpam-6138	243	14	0	0	NUM
ejpam-6138	243	15	,	,	PUNCT
ejpam-6138	243	16	ζ	ζ	NOUN
ejpam-6138	243	17	=	=	SYM
ejpam-6138	243	18	2	2	NUM
ejpam-6138	243	19	>	>	SYM
ejpam-6138	243	20	0	0	X
ejpam-6138	243	21	.	.	PUNCT
ejpam-6138	244	1	moreover	moreover	ADV
ejpam-6138	244	2	,	,	PUNCT
ejpam-6138	244	3	we	we	PRON
ejpam-6138	244	4	have	have	VERB
ejpam-6138	244	5	ϖ	ϖ	NOUN
ejpam-6138	244	6	=	=	SYM
ejpam-6138	244	7	ζ	ζ	NOUN
ejpam-6138	244	8	ϱσγ(σ+1	ϱσγ(σ+1	PROPN
ejpam-6138	244	9	)	)	PUNCT
ejpam-6138	244	10	[	[	PUNCT
ejpam-6138	244	11	ϑ	ϑ	X
ejpam-6138	244	12	ϱσ	ϱσ	NOUN
ejpam-6138	244	13	σ1/(σ−1	σ1/(σ−1	PROPN
ejpam-6138	244	14	)	)	PUNCT
ejpam-6138	244	15	−	−	PROPN
ejpam-6138	244	16	ϑ	ϑ	PROPN
ejpam-6138	244	17	ϱσ	ϱσ	NOUN
ejpam-6138	244	18	σσ/(σ−1	σσ/(σ−1	NUM
ejpam-6138	244	19	)	)	PUNCT
ejpam-6138	244	20	]	]	PUNCT
ejpam-6138	245	1	+	+	CCONJ
ejpam-6138	245	2	η	η	PROPN
ejpam-6138	245	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	245	4	)	)	PUNCT
ejpam-6138	246	1	[	[	X
ejpam-6138	246	2	ϑ	ϑ	X
ejpam-6138	246	3	(	(	PUNCT
ejpam-6138	246	4	ϱσ−1	ϱσ−1	PROPN
ejpam-6138	246	5	)	)	PUNCT
ejpam-6138	246	6	(	(	PUNCT
ejpam-6138	246	7	ϱ−1	ϱ−1	PROPN
ejpam-6138	246	8	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	246	9	)	)	PUNCT
ejpam-6138	246	10	)	)	PUNCT
ejpam-6138	246	11	(	(	PUNCT
ejpam-6138	246	12	ϱ−1)/ϱ(σ−1	ϱ−1)/ϱ(σ−1	NOUN
ejpam-6138	246	13	)	)	PUNCT
ejpam-6138	246	14	−σ(ϑ)(ϱσ−1	−σ(ϑ)(ϱσ−1	NUM
ejpam-6138	246	15	)	)	PUNCT
ejpam-6138	246	16	(	(	PUNCT
ejpam-6138	246	17	ϱ−1	ϱ−1	PROPN
ejpam-6138	246	18	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	246	19	)	)	PUNCT
ejpam-6138	246	20	)	)	PUNCT
ejpam-6138	246	21	(	(	PUNCT
ejpam-6138	246	22	ϱσ−1)/ϱ(σ−1	ϱσ−1)/ϱ(σ−1	X
ejpam-6138	246	23	)	)	PUNCT
ejpam-6138	246	24	]	]	PUNCT
ejpam-6138	247	1	≈	≈	PROPN
ejpam-6138	247	2	⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩	⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩	PROPN
ejpam-6138	247	3	0.9751	0.9751	NUM
ejpam-6138	247	4	,	,	PUNCT
ejpam-6138	247	5	σ	σ	X
ejpam-6138	247	6	=	=	SYM
ejpam-6138	247	7	1.50	1.50	NUM
ejpam-6138	247	8	,	,	PUNCT
ejpam-6138	247	9	0.9188	0.9188	NUM
ejpam-6138	247	10	,	,	PUNCT
ejpam-6138	247	11	σ	σ	NOUN
ejpam-6138	247	12	=	=	SYM
ejpam-6138	247	13	1.65	1.65	NUM
ejpam-6138	247	14	,	,	PUNCT
ejpam-6138	247	15	0.8508	0.8508	NUM
ejpam-6138	247	16	,	,	PUNCT
ejpam-6138	247	17	σ	σ	NOUN
ejpam-6138	247	18	=	=	SYM
ejpam-6138	247	19	1.80	1.80	NUM
ejpam-6138	247	20	,	,	PUNCT
ejpam-6138	247	21	0.7758	0.7758	NUM
ejpam-6138	247	22	,	,	PUNCT
ejpam-6138	247	23	σ	σ	NOUN
ejpam-6138	247	24	=	=	SYM
ejpam-6138	247	25	1.95	1.95	NUM
ejpam-6138	247	26	,	,	PUNCT
ejpam-6138	247	27	⎫⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎭	⎫⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎭	PRON
ejpam-6138	247	28	<	<	X
ejpam-6138	247	29	1	1	X
ejpam-6138	247	30	.	.	PUNCT
ejpam-6138	248	1	the	the	DET
ejpam-6138	248	2	curves	curve	NOUN
ejpam-6138	248	3	drawn	draw	VERB
ejpam-6138	248	4	in	in	ADP
ejpam-6138	248	5	figure	figure	NOUN
ejpam-6138	248	6	1	1	NUM
ejpam-6138	248	7	show	show	VERB
ejpam-6138	248	8	how	how	SCONJ
ejpam-6138	248	9	the	the	DET
ejpam-6138	248	10	ϖ	ϖ	NOUN
ejpam-6138	248	11	changes	change	NOUN
ejpam-6138	248	12	for	for	ADP
ejpam-6138	248	13	different	different	ADJ
ejpam-6138	248	14	derivative	derivative	ADJ
ejpam-6138	248	15	orders	order	NOUN
ejpam-6138	248	16	σ	σ	NOUN
ejpam-6138	248	17	.	.	PUNCT
ejpam-6138	249	1	the	the	DET
ejpam-6138	249	2	important	important	ADJ
ejpam-6138	249	3	point	point	NOUN
ejpam-6138	249	4	is	be	AUX
ejpam-6138	249	5	that	that	SCONJ
ejpam-6138	249	6	all	all	PRON
ejpam-6138	249	7	of	of	ADP
ejpam-6138	249	8	them	they	PRON
ejpam-6138	249	9	are	be	AUX
ejpam-6138	249	10	less	less	ADJ
ejpam-6138	249	11	than	than	ADP
ejpam-6138	249	12	the	the	DET
ejpam-6138	249	13	line	line	NOUN
ejpam-6138	249	14	y	y	NOUN
ejpam-6138	249	15	=	=	NOUN
ejpam-6138	249	16	1	1	NUM
ejpam-6138	249	17	in	in	ADP
ejpam-6138	249	18	the	the	DET
ejpam-6138	249	19	interval	interval	NOUN
ejpam-6138	249	20	[	[	X
ejpam-6138	249	21	0	0	NUM
ejpam-6138	249	22	,	,	PUNCT
ejpam-6138	249	23	ϑ	ϑ	X
ejpam-6138	249	24	]	]	X
ejpam-6138	249	25	,	,	PUNCT
ejpam-6138	249	26	and	and	CCONJ
ejpam-6138	249	27	as	as	SCONJ
ejpam-6138	249	28	the	the	DET
ejpam-6138	249	29	order	order	NOUN
ejpam-6138	249	30	of	of	ADP
ejpam-6138	249	31	the	the	DET
ejpam-6138	249	32	derivative	derivative	ADJ
ejpam-6138	249	33	approaches	approach	VERB
ejpam-6138	249	34	the	the	DET
ejpam-6138	249	35	number	number	NOUN
ejpam-6138	249	36	one	one	NUM
ejpam-6138	249	37	,	,	PUNCT
ejpam-6138	249	38	the	the	DET
ejpam-6138	249	39	parameter	parameter	NOUN
ejpam-6138	249	40	ϖ	ϖ	PROPN
ejpam-6138	249	41	decreases	decrease	VERB
ejpam-6138	249	42	,	,	PUNCT
ejpam-6138	249	43	but	but	CCONJ
ejpam-6138	249	44	they	they	PRON
ejpam-6138	249	45	are	be	AUX
ejpam-6138	249	46	still	still	ADV
ejpam-6138	249	47	less	less	ADJ
ejpam-6138	249	48	than	than	ADP
ejpam-6138	249	49	one	one	NUM
ejpam-6138	249	50	.	.	PUNCT
ejpam-6138	250	1	these	these	DET
ejpam-6138	250	2	results	result	NOUN
ejpam-6138	250	3	are	be	AUX
ejpam-6138	250	4	shown	show	VERB
ejpam-6138	250	5	in	in	ADP
ejpam-6138	250	6	table	table	NOUN
ejpam-6138	250	7	1	1	NUM
ejpam-6138	250	8	.	.	PUNCT
ejpam-6138	250	9	by	by	ADP
ejpam-6138	250	10	the	the	DET
ejpam-6138	250	11	applications	application	NOUN
ejpam-6138	250	12	of	of	ADP
ejpam-6138	250	13	theorem	theorem	NOUN
ejpam-6138	250	14	2	2	NUM
ejpam-6138	250	15	,	,	PUNCT
ejpam-6138	250	16	and	and	CCONJ
ejpam-6138	250	17	the	the	DET
ejpam-6138	250	18	condition	condition	NOUN
ejpam-6138	250	19	(	(	PUNCT
ejpam-6138	250	20	3.12	3.12	NUM
ejpam-6138	250	21	)	)	PUNCT
ejpam-6138	250	22	is	be	AUX
ejpam-6138	250	23	agreed	agree	VERB
ejpam-6138	250	24	.	.	PUNCT
ejpam-6138	251	1	then	then	ADV
ejpam-6138	251	2	the	the	DET
ejpam-6138	251	3	bvp	bvp	PROPN
ejpam-6138	251	4	(	(	PUNCT
ejpam-6138	251	5	4.1	4.1	NUM
ejpam-6138	251	6	)	)	PUNCT
ejpam-6138	251	7	accepts	accept	VERB
ejpam-6138	251	8	an	an	DET
ejpam-6138	251	9	unique	unique	ADJ
ejpam-6138	251	10	solution	solution	NOUN
ejpam-6138	251	11	.	.	PUNCT
ejpam-6138	252	1	z.	z.	PROPN
ejpam-6138	252	2	bekri	bekri	PROPN
ejpam-6138	252	3	et	et	PROPN
ejpam-6138	252	4	al	al	PROPN
ejpam-6138	252	5	.	.	PUNCT
ejpam-6138	252	6	/	/	SYM
ejpam-6138	252	7	eur	eur	PROPN
ejpam-6138	252	8	.	.	PUNCT
ejpam-6138	253	1	j.	j.	PROPN
ejpam-6138	253	2	pure	pure	PROPN
ejpam-6138	253	3	appl	appl	PROPN
ejpam-6138	253	4	.	.	PROPN
ejpam-6138	253	5	math	math	PROPN
ejpam-6138	253	6	,	,	PUNCT
ejpam-6138	253	7	18	18	NUM
ejpam-6138	253	8	(	(	PUNCT
ejpam-6138	253	9	2	2	NUM
ejpam-6138	253	10	)	)	PUNCT
ejpam-6138	253	11	(	(	PUNCT
ejpam-6138	253	12	2025	2025	NUM
ejpam-6138	253	13	)	)	PUNCT
ejpam-6138	253	14	,	,	PUNCT
ejpam-6138	253	15	6138	6138	NUM
ejpam-6138	253	16	12	12	NUM
ejpam-6138	253	17	of	of	ADP
ejpam-6138	253	18	17	17	NUM
ejpam-6138	253	19	table	table	NOUN
ejpam-6138	253	20	1	1	NUM
ejpam-6138	253	21	:	:	PUNCT
ejpam-6138	253	22	numerical	numerical	ADJ
ejpam-6138	253	23	results	result	NOUN
ejpam-6138	253	24	ϖ	ϖ	VERB
ejpam-6138	253	25	in	in	ADP
ejpam-6138	253	26	example	example	NOUN
ejpam-6138	253	27	1	1	NUM
ejpam-6138	253	28	for	for	ADP
ejpam-6138	253	29	four	four	NUM
ejpam-6138	253	30	values	value	NOUN
ejpam-6138	253	31	of	of	ADP
ejpam-6138	253	32	σ	σ	PROPN
ejpam-6138	253	33	.	.	PUNCT
ejpam-6138	254	1	τ	τ	PROPN
ejpam-6138	254	2	ϖ	ϖ	PROPN
ejpam-6138	254	3	σ	σ	NOUN
ejpam-6138	255	1	=	=	SYM
ejpam-6138	255	2	1.5σ	1.5σ	PROPN
ejpam-6138	255	3	=	=	SYM
ejpam-6138	255	4	1.5σ	1.5σ	NUM
ejpam-6138	255	5	=	=	SYM
ejpam-6138	255	6	1.5	1.5	NUM
ejpam-6138	255	7	σ	σ	NOUN
ejpam-6138	255	8	=	=	SYM
ejpam-6138	255	9	1.65σ	1.65σ	NUM
ejpam-6138	255	10	=	=	SYM
ejpam-6138	255	11	1.65σ	1.65σ	NUM
ejpam-6138	255	12	=	=	SYM
ejpam-6138	255	13	1.65	1.65	NUM
ejpam-6138	255	14	σ	σ	NOUN
ejpam-6138	255	15	=	=	SYM
ejpam-6138	255	16	1.80σ	1.80σ	NUM
ejpam-6138	255	17	=	=	SYM
ejpam-6138	255	18	1.80σ	1.80σ	NUM
ejpam-6138	255	19	=	=	SYM
ejpam-6138	255	20	1.80	1.80	NUM
ejpam-6138	255	21	σ	σ	NOUN
ejpam-6138	255	22	=	=	SYM
ejpam-6138	255	23	1.95σ	1.95σ	NUM
ejpam-6138	255	24	=	=	SYM
ejpam-6138	255	25	1.95σ	1.95σ	NUM
ejpam-6138	255	26	=	=	SYM
ejpam-6138	255	27	1.95	1.95	NUM
ejpam-6138	255	28	0.00	0.00	NUM
ejpam-6138	255	29	0.0000	0.0000	NUM
ejpam-6138	255	30	0.0000	0.0000	NUM
ejpam-6138	255	31	0.0000	0.0000	NUM
ejpam-6138	255	32	0.0000	0.0000	NUM
ejpam-6138	255	33	0.05	0.05	NUM
ejpam-6138	255	34	0.1707	0.1707	NUM
ejpam-6138	255	35	0.0978	0.0978	NUM
ejpam-6138	255	36	0.0555	0.0555	NUM
ejpam-6138	255	37	0.0311	0.0311	NUM
ejpam-6138	255	38	0.10	0.10	NUM
ejpam-6138	255	39	0.2449	0.2449	NUM
ejpam-6138	255	40	0.1562	0.1562	NUM
ejpam-6138	255	41	0.0986	0.0986	NUM
ejpam-6138	255	42	0.0616	0.0616	NUM
ejpam-6138	255	43	0.15	0.15	NUM
ejpam-6138	255	44	0.3043	0.3043	NUM
ejpam-6138	255	45	0.2069	0.2069	NUM
ejpam-6138	255	46	0.1391	0.1391	NUM
ejpam-6138	255	47	0.0926	0.0926	NUM
ejpam-6138	255	48	0.20	0.20	NUM
ejpam-6138	255	49	0.3564	0.3564	NUM
ejpam-6138	255	50	0.2538	0.2538	NUM
ejpam-6138	255	51	0.1786	0.1786	NUM
ejpam-6138	255	52	0.1244	0.1244	NUM
ejpam-6138	255	53	0.25	0.25	NUM
ejpam-6138	255	54	0.4040	0.4040	NUM
ejpam-6138	255	55	0.2984	0.2984	NUM
ejpam-6138	255	56	0.2177	0.2177	NUM
ejpam-6138	255	57	0.1571	0.1571	NUM
ejpam-6138	255	58	0.30	0.30	NUM
ejpam-6138	255	59	0.4487	0.4487	NUM
ejpam-6138	255	60	0.3415	0.3415	NUM
ejpam-6138	255	61	0.2568	0.2568	NUM
ejpam-6138	255	62	0.1909	0.1909	NUM
ejpam-6138	255	63	0.35	0.35	NUM
ejpam-6138	255	64	0.4912	0.4912	NUM
ejpam-6138	255	65	0.3837	0.3837	NUM
ejpam-6138	255	66	0.2960	0.2960	NUM
ejpam-6138	255	67	0.2256	0.2256	NUM
ejpam-6138	255	68	0.40	0.40	NUM
ejpam-6138	255	69	0.5322	0.5322	NUM
ejpam-6138	255	70	0.4253	0.4253	NUM
ejpam-6138	256	1	0.3355	0.3355	NUM
ejpam-6138	256	2	0.2614	0.2614	NUM
ejpam-6138	256	3	0.45	0.45	NUM
ejpam-6138	256	4	0.5719	0.5719	NUM
ejpam-6138	256	5	0.4664	0.4664	NUM
ejpam-6138	256	6	0.3753	0.3753	NUM
ejpam-6138	256	7	0.2983	0.2983	NUM
ejpam-6138	256	8	0.50	0.50	NUM
ejpam-6138	257	1	0.6107	0.6107	NUM
ejpam-6138	257	2	0.5073	0.5073	NUM
ejpam-6138	257	3	0.4156	0.4156	NUM
ejpam-6138	257	4	0.3362	0.3362	NUM
ejpam-6138	257	5	0.55	0.55	NUM
ejpam-6138	257	6	0.6488	0.6488	NUM
ejpam-6138	257	7	0.5481	0.5481	NUM
ejpam-6138	257	8	0.4564	0.4564	NUM
ejpam-6138	257	9	0.3753	0.3753	NUM
ejpam-6138	257	10	0.60	0.60	NUM
ejpam-6138	257	11	0.6863	0.6863	NUM
ejpam-6138	257	12	0.5888	0.5888	NUM
ejpam-6138	257	13	0.4978	0.4978	NUM
ejpam-6138	257	14	0.4154	0.4154	NUM
ejpam-6138	257	15	0.65	0.65	NUM
ejpam-6138	257	16	0.7233	0.7233	NUM
ejpam-6138	257	17	0.6295	0.6295	NUM
ejpam-6138	257	18	0.5397	0.5397	NUM
ejpam-6138	257	19	0.4566	0.4566	NUM
ejpam-6138	257	20	0.70	0.70	NUM
ejpam-6138	257	21	0.7599	0.7599	NUM
ejpam-6138	257	22	0.6703	0.6703	NUM
ejpam-6138	257	23	0.5822	0.5822	NUM
ejpam-6138	257	24	0.4989	0.4989	NUM
ejpam-6138	257	25	0.75	0.75	NUM
ejpam-6138	257	26	0.7962	0.7962	NUM
ejpam-6138	257	27	0.7112	0.7112	NUM
ejpam-6138	257	28	0.6254	0.6254	NUM
ejpam-6138	257	29	0.5423	0.5423	NUM
ejpam-6138	257	30	0.80	0.80	NUM
ejpam-6138	257	31	0.8323	0.8323	NUM
ejpam-6138	257	32	0.7523	0.7523	NUM
ejpam-6138	257	33	0.6691	0.6691	NUM
ejpam-6138	257	34	0.5868	0.5868	NUM
ejpam-6138	257	35	0.85	0.85	NUM
ejpam-6138	257	36	0.8682	0.8682	NUM
ejpam-6138	257	37	0.7936	0.7936	NUM
ejpam-6138	257	38	0.7136	0.7136	NUM
ejpam-6138	257	39	0.6324	0.6324	NUM
ejpam-6138	257	40	0.90	0.90	NUM
ejpam-6138	257	41	0.9040	0.9040	NUM
ejpam-6138	257	42	0.8351	0.8351	NUM
ejpam-6138	257	43	0.7586	0.7586	NUM
ejpam-6138	257	44	0.6791	0.6791	NUM
ejpam-6138	257	45	0.95	0.95	NUM
ejpam-6138	257	46	0.9396	0.9396	NUM
ejpam-6138	257	47	0.8768	0.8768	NUM
ejpam-6138	257	48	0.8044	0.8044	NUM
ejpam-6138	258	1	0.7269	0.7269	NUM
ejpam-6138	258	2	1.00	1.00	NUM
ejpam-6138	258	3	0.9751	0.9751	NUM
ejpam-6138	258	4	0.9188	0.9188	NUM
ejpam-6138	258	5	0.8508	0.8508	NUM
ejpam-6138	258	6	0.7758	0.7758	NUM
ejpam-6138	258	7	τ	τ	X
ejpam-6138	258	8	0	0	NUM
ejpam-6138	258	9	0.1	0.1	NUM
ejpam-6138	258	10	0.2	0.2	NUM
ejpam-6138	258	11	0.3	0.3	NUM
ejpam-6138	258	12	0.4	0.4	NUM
ejpam-6138	258	13	0.5	0.5	NUM
ejpam-6138	258	14	0.6	0.6	NUM
ejpam-6138	258	15	0.7	0.7	NUM
ejpam-6138	258	16	0.8	0.8	NUM
ejpam-6138	258	17	0.9	0.9	NUM
ejpam-6138	258	18	1	1	NUM
ejpam-6138	258	19	̟	̟	PROPN
ejpam-6138	258	20	0	0	NUM
ejpam-6138	258	21	0.1	0.1	NUM
ejpam-6138	258	22	0.2	0.2	NUM
ejpam-6138	258	23	0.3	0.3	NUM
ejpam-6138	258	24	0.4	0.4	NUM
ejpam-6138	258	25	0.5	0.5	NUM
ejpam-6138	258	26	0.6	0.6	NUM
ejpam-6138	258	27	0.7	0.7	NUM
ejpam-6138	258	28	0.8	0.8	NUM
ejpam-6138	258	29	0.9	0.9	NUM
ejpam-6138	258	30	1	1	NUM
ejpam-6138	258	31	̟	̟	PROPN
ejpam-6138	258	32	<	<	X
ejpam-6138	258	33	1	1	NUM
ejpam-6138	258	34	σ=1.50	σ=1.50	X
ejpam-6138	258	35	σ=1.65	σ=1.65	ADV
ejpam-6138	258	36	σ=1.80	σ=1.80	NOUN
ejpam-6138	258	37	σ=1.95	σ=1.95	NOUN
ejpam-6138	258	38	figure	figure	NOUN
ejpam-6138	258	39	1	1	NUM
ejpam-6138	258	40	:	:	PUNCT
ejpam-6138	258	41	representation	representation	NOUN
ejpam-6138	258	42	of	of	ADP
ejpam-6138	258	43	ϖ	ϖ	PROPN
ejpam-6138	258	44	for	for	ADP
ejpam-6138	258	45	bvp	bvp	NOUN
ejpam-6138	258	46	(	(	PUNCT
ejpam-6138	258	47	4.1	4.1	NUM
ejpam-6138	258	48	)	)	PUNCT
ejpam-6138	258	49	in	in	ADP
ejpam-6138	258	50	example	example	NOUN
ejpam-6138	258	51	1	1	NUM
ejpam-6138	258	52	for	for	ADP
ejpam-6138	258	53	four	four	NUM
ejpam-6138	258	54	case	case	NOUN
ejpam-6138	258	55	σ	σ	PROPN
ejpam-6138	258	56	.	.	PROPN
ejpam-6138	258	57	example	example	NOUN
ejpam-6138	258	58	2	2	NUM
ejpam-6138	258	59	.	.	PUNCT
ejpam-6138	258	60	extrapolate	extrapolate	VERB
ejpam-6138	258	61	the	the	DET
ejpam-6138	258	62	following	follow	VERB
ejpam-6138	258	63	application	application	NOUN
ejpam-6138	258	64	of	of	ADP
ejpam-6138	258	65	bvp	bvp	PROPN
ejpam-6138	258	66	{	{	PUNCT
ejpam-6138	258	67	1	1	NUM
ejpam-6138	258	68	cd	cd	PROPN
ejpam-6138	258	69	σ	σ	PROPN
ejpam-6138	258	70	0+µ(τ	0+µ(τ	PROPN
ejpam-6138	258	71	)	)	PUNCT
ejpam-6138	259	1	=	=	SYM
ejpam-6138	259	2	2	2	NUM
ejpam-6138	259	3	−	−	NOUN
ejpam-6138	259	4	τ	τ	X
ejpam-6138	259	5	3	3	NUM
ejpam-6138	259	6	+	+	CCONJ
ejpam-6138	259	7	1	1	NUM
ejpam-6138	259	8	2	2	NUM
ejpam-6138	259	9	cos(µ(τ	cos(µ(τ	NOUN
ejpam-6138	259	10	)	)	PUNCT
ejpam-6138	259	11	)	)	PUNCT
ejpam-6138	259	12	−	−	PROPN
ejpam-6138	259	13	1	1	NUM
ejpam-6138	259	14	cd	cd	NOUN
ejpam-6138	259	15	1	1	NUM
ejpam-6138	259	16	0	0	NUM
ejpam-6138	259	17	+	+	NUM
ejpam-6138	259	18	sin(µ(τ	sin(µ(τ	NOUN
ejpam-6138	259	19	)	)	PUNCT
ejpam-6138	259	20	)	)	PUNCT
ejpam-6138	259	21	,	,	PUNCT
ejpam-6138	259	22	0	0	PUNCT
ejpam-6138	259	23	<	<	X
ejpam-6138	259	24	τ	τ	X
ejpam-6138	259	25	<	<	X
ejpam-6138	259	26	ϑ	ϑ	X
ejpam-6138	259	27	µ(0	µ(0	NOUN
ejpam-6138	259	28	)	)	PUNCT
ejpam-6138	259	29	=	=	SYM
ejpam-6138	259	30	5	5	NUM
ejpam-6138	259	31	,	,	PUNCT
ejpam-6138	259	32	µ(1	µ(1	PROPN
ejpam-6138	259	33	)	)	PUNCT
ejpam-6138	259	34	=	=	NOUN
ejpam-6138	259	35	6	6	NUM
ejpam-6138	259	36	.	.	PUNCT
ejpam-6138	260	1	(	(	PUNCT
ejpam-6138	260	2	4.2	4.2	NUM
ejpam-6138	260	3	)	)	PUNCT
ejpam-6138	260	4	z.	z.	PROPN
ejpam-6138	260	5	bekri	bekri	PROPN
ejpam-6138	260	6	et	et	PROPN
ejpam-6138	260	7	al	al	PROPN
ejpam-6138	260	8	.	.	PUNCT
ejpam-6138	260	9	/	/	SYM
ejpam-6138	260	10	eur	eur	PROPN
ejpam-6138	260	11	.	.	PUNCT
ejpam-6138	261	1	j.	j.	PROPN
ejpam-6138	261	2	pure	pure	PROPN
ejpam-6138	261	3	appl	appl	PROPN
ejpam-6138	261	4	.	.	PROPN
ejpam-6138	261	5	math	math	PROPN
ejpam-6138	261	6	,	,	PUNCT
ejpam-6138	261	7	18	18	NUM
ejpam-6138	261	8	(	(	PUNCT
ejpam-6138	261	9	2	2	NUM
ejpam-6138	261	10	)	)	PUNCT
ejpam-6138	261	11	(	(	PUNCT
ejpam-6138	261	12	2025	2025	NUM
ejpam-6138	261	13	)	)	PUNCT
ejpam-6138	261	14	,	,	PUNCT
ejpam-6138	261	15	6138	6138	NUM
ejpam-6138	261	16	13	13	NUM
ejpam-6138	261	17	of	of	ADP
ejpam-6138	261	18	17	17	NUM
ejpam-6138	261	19	set	set	NOUN
ejpam-6138	261	20	,	,	PUNCT
ejpam-6138	261	21	ϱ	ϱ	X
ejpam-6138	261	22	=	=	SYM
ejpam-6138	261	23	1	1	NUM
ejpam-6138	261	24	,	,	PUNCT
ejpam-6138	261	25	σ	σ	PROPN
ejpam-6138	261	26	∈	∈	PROPN
ejpam-6138	261	27	{	{	PUNCT
ejpam-6138	261	28	4	4	NUM
ejpam-6138	261	29	3	3	NUM
ejpam-6138	261	30	,	,	PUNCT
ejpam-6138	261	31	3	3	NUM
ejpam-6138	261	32	2	2	NUM
ejpam-6138	261	33	,	,	PUNCT
ejpam-6138	261	34	7	7	NUM
ejpam-6138	261	35	4	4	NUM
ejpam-6138	261	36	}	}	PUNCT
ejpam-6138	261	37	,	,	PUNCT
ejpam-6138	261	38	ς	ς	PROPN
ejpam-6138	261	39	=	=	SYM
ejpam-6138	261	40	1	1	NUM
ejpam-6138	261	41	,	,	PUNCT
ejpam-6138	261	42	θ	θ	PROPN
ejpam-6138	261	43	=	=	SYM
ejpam-6138	261	44	0	0	NUM
ejpam-6138	261	45	,	,	PUNCT
ejpam-6138	261	46	ϑ	ϑ	X
ejpam-6138	261	47	=	=	SYM
ejpam-6138	261	48	1	1	NUM
ejpam-6138	261	49	,	,	PUNCT
ejpam-6138	261	50	and	and	CCONJ
ejpam-6138	261	51	ξ	ξ	X
ejpam-6138	261	52	(	(	PUNCT
ejpam-6138	261	53	τ	τ	PROPN
ejpam-6138	261	54	,	,	PUNCT
ejpam-6138	261	55	µ(τ	µ(τ	PROPN
ejpam-6138	261	56	)	)	PUNCT
ejpam-6138	261	57	,	,	PUNCT
ejpam-6138	261	58	ϱcdς	ϱcdς	ADJ
ejpam-6138	261	59	θ+µ(τ	θ+µ(τ	NOUN
ejpam-6138	261	60	)	)	PUNCT
ejpam-6138	261	61	)	)	PUNCT
ejpam-6138	262	1	=	=	PUNCT
ejpam-6138	262	2	τ	τ	X
ejpam-6138	262	3	3	3	NUM
ejpam-6138	262	4	−	−	NOUN
ejpam-6138	262	5	2	2	NUM
ejpam-6138	262	6	−	−	NOUN
ejpam-6138	262	7	1	1	NUM
ejpam-6138	262	8	2	2	NUM
ejpam-6138	262	9	cos(µ(τ	cos(µ(τ	NOUN
ejpam-6138	262	10	)	)	PUNCT
ejpam-6138	262	11	)	)	PUNCT
ejpam-6138	263	1	+	+	CCONJ
ejpam-6138	263	2	1	1	NUM
ejpam-6138	263	3	cd	cd	NOUN
ejpam-6138	263	4	1	1	NUM
ejpam-6138	263	5	0	0	NUM
ejpam-6138	263	6	+	+	NUM
ejpam-6138	263	7	sin	sin	NOUN
ejpam-6138	263	8	(	(	PUNCT
ejpam-6138	263	9	µ(τ	µ(τ	PROPN
ejpam-6138	263	10	)	)	PUNCT
ejpam-6138	263	11	)	)	PUNCT
ejpam-6138	263	12	.	.	PUNCT
ejpam-6138	264	1	here	here	ADV
ejpam-6138	264	2	,	,	PUNCT
ejpam-6138	264	3	»	»	PUNCT
ejpam-6138	264	4	»	»	PUNCT
ejpam-6138	264	5	»	»	PRON
ejpam-6138	264	6	»	»	PRON
ejpam-6138	264	7	»	»	ADV
ejpam-6138	264	8	»	»	PUNCT
ejpam-6138	264	9	ξ(τ	ξ(τ	PROPN
ejpam-6138	264	10	,	,	PUNCT
ejpam-6138	264	11	µ	µ	NOUN
ejpam-6138	264	12	,	,	PUNCT
ejpam-6138	264	13	µ	µ	NOUN
ejpam-6138	264	14	′	′	NUM
ejpam-6138	264	15	)	)	PUNCT
ejpam-6138	264	16	−	−	PROPN
ejpam-6138	264	17	ξ(τ	ξ(τ	PROPN
ejpam-6138	264	18	,	,	PUNCT
ejpam-6138	264	19	ν	ν	NOUN
ejpam-6138	264	20	,	,	PUNCT
ejpam-6138	264	21	ν	ν	NOUN
ejpam-6138	264	22	′	′	NUM
ejpam-6138	264	23	)	)	PUNCT
ejpam-6138	265	1	»	»	NOUN
ejpam-6138	265	2	»	»	PUNCT
ejpam-6138	265	3	»	»	PUNCT
ejpam-6138	265	4	»	»	PRON
ejpam-6138	265	5	»	»	PUNCT
ejpam-6138	265	6	»	»	PUNCT
ejpam-6138	265	7	=	=	NOUN
ejpam-6138	265	8	»	»	X
ejpam-6138	265	9	»	»	PUNCT
ejpam-6138	265	10	»	»	PUNCT
ejpam-6138	265	11	»	»	PUNCT
ejpam-6138	265	12	»	»	PUNCT
ejpam-6138	265	13	»	»	X
ejpam-6138	265	14	τ	τ	X
ejpam-6138	265	15	3	3	NUM
ejpam-6138	265	16	−	−	NOUN
ejpam-6138	265	17	2	2	NUM
ejpam-6138	265	18	−	−	NOUN
ejpam-6138	265	19	1	1	NUM
ejpam-6138	265	20	2	2	NUM
ejpam-6138	265	21	cos(µ	cos(µ	PROPN
ejpam-6138	265	22	)	)	PUNCT
ejpam-6138	265	23	+	+	NUM
ejpam-6138	265	24	sin	sin	NOUN
ejpam-6138	265	25	(	(	PUNCT
ejpam-6138	265	26	µ′	µ′	NOUN
ejpam-6138	265	27	)	)	PUNCT
ejpam-6138	265	28	−	−	PROPN
ejpam-6138	266	1	(	(	PUNCT
ejpam-6138	266	2	τ3	τ3	NOUN
ejpam-6138	266	3	−	−	NOUN
ejpam-6138	266	4	2	2	NUM
ejpam-6138	266	5	−	−	NOUN
ejpam-6138	266	6	1	1	NUM
ejpam-6138	266	7	2	2	NUM
ejpam-6138	266	8	cos(ν	cos(ν	NUM
ejpam-6138	266	9	)	)	PUNCT
ejpam-6138	267	1	+	+	NUM
ejpam-6138	267	2	sin	sin	NOUN
ejpam-6138	267	3	(	(	PUNCT
ejpam-6138	267	4	ν	ν	NOUN
ejpam-6138	267	5	′	′	NUM
ejpam-6138	267	6	)	)	PUNCT
ejpam-6138	267	7	)	)	PUNCT
ejpam-6138	268	1	»	»	ADP
ejpam-6138	268	2	»	»	PUNCT
ejpam-6138	268	3	»	»	PUNCT
ejpam-6138	268	4	»	»	PRON
ejpam-6138	268	5	»	»	ADV
ejpam-6138	268	6	»	»	NOUN
ejpam-6138	268	7	≤	≤	NUM
ejpam-6138	268	8	1	1	NUM
ejpam-6138	268	9	2	2	NUM
ejpam-6138	268	10	»	»	NOUN
ejpam-6138	268	11	»	»	PUNCT
ejpam-6138	268	12	»	»	PRON
ejpam-6138	268	13	»	»	PRON
ejpam-6138	268	14	»	»	ADJ
ejpam-6138	268	15	»	»	X
ejpam-6138	268	16	cos(ν	cos(ν	PROPN
ejpam-6138	268	17	)	)	PUNCT
ejpam-6138	268	18	−	−	PROPN
ejpam-6138	268	19	cos(µ	cos(µ	PROPN
ejpam-6138	268	20	)	)	PUNCT
ejpam-6138	268	21	»	»	PUNCT
ejpam-6138	268	22	»	»	PUNCT
ejpam-6138	268	23	»	»	PUNCT
ejpam-6138	268	24	»	»	PRON
ejpam-6138	268	25	»	»	PRON
ejpam-6138	268	26	»	»	PUNCT
ejpam-6138	268	27	+	+	ADJ
ejpam-6138	268	28	»	»	PUNCT
ejpam-6138	268	29	»	»	PRON
ejpam-6138	268	30	»	»	PRON
ejpam-6138	268	31	»	»	PRON
ejpam-6138	268	32	»	»	PRON
ejpam-6138	268	33	»	»	X
ejpam-6138	268	34	sin	sin	NOUN
ejpam-6138	268	35	(	(	PUNCT
ejpam-6138	268	36	µ	µ	NOUN
ejpam-6138	268	37	′	′	NUM
ejpam-6138	268	38	)	)	PUNCT
ejpam-6138	268	39	−	−	PROPN
ejpam-6138	268	40	sin	sin	NOUN
ejpam-6138	268	41	(	(	PUNCT
ejpam-6138	268	42	ν	ν	NOUN
ejpam-6138	268	43	′	′	NUM
ejpam-6138	268	44	)	)	PUNCT
ejpam-6138	268	45	»	»	PRON
ejpam-6138	268	46	»	»	PUNCT
ejpam-6138	268	47	»	»	PUNCT
ejpam-6138	268	48	»	»	PRON
ejpam-6138	268	49	»	»	ADV
ejpam-6138	268	50	»	»	NOUN
ejpam-6138	268	51	≤	≤	NUM
ejpam-6138	268	52	1	1	NUM
ejpam-6138	268	53	2	2	NUM
ejpam-6138	268	54	»	»	NOUN
ejpam-6138	268	55	»	»	PUNCT
ejpam-6138	268	56	»	»	PRON
ejpam-6138	268	57	»	»	PRON
ejpam-6138	268	58	»	»	PUNCT
ejpam-6138	268	59	»	»	PUNCT
ejpam-6138	268	60	−	−	PROPN
ejpam-6138	268	61	2	2	NUM
ejpam-6138	268	62	sin	sin	NOUN
ejpam-6138	268	63	ν+µ	ν+µ	NOUN
ejpam-6138	268	64	2	2	NUM
ejpam-6138	268	65	sin	sin	NOUN
ejpam-6138	268	66	ν−µ	ν−µ	NOUN
ejpam-6138	268	67	2	2	NUM
ejpam-6138	268	68	»	»	NOUN
ejpam-6138	268	69	»	»	PRON
ejpam-6138	268	70	»	»	PRON
ejpam-6138	268	71	»	»	PRON
ejpam-6138	268	72	»	»	PRON
ejpam-6138	268	73	»	»	PUNCT
ejpam-6138	268	74	+	+	ADJ
ejpam-6138	268	75	»	»	PUNCT
ejpam-6138	268	76	»	»	PRON
ejpam-6138	268	77	»	»	PUNCT
ejpam-6138	268	78	»	»	PRON
ejpam-6138	268	79	»	»	X
ejpam-6138	268	80	µ	µ	NOUN
ejpam-6138	268	81	′	′	NOUN
ejpam-6138	268	82	−	−	PROPN
ejpam-6138	268	83	ν	ν	NOUN
ejpam-6138	268	84	′	′	NUM
ejpam-6138	268	85	»	»	PUNCT
ejpam-6138	268	86	»	»	PUNCT
ejpam-6138	268	87	»	»	PRON
ejpam-6138	268	88	»	»	ADV
ejpam-6138	268	89	»	»	X
ejpam-6138	268	90	≤	≤	NOUN
ejpam-6138	268	91	»	»	PUNCT
ejpam-6138	268	92	»	»	PUNCT
ejpam-6138	268	93	»	»	PRON
ejpam-6138	268	94	»	»	PRON
ejpam-6138	268	95	»	»	PUNCT
ejpam-6138	268	96	sin	sin	VERB
ejpam-6138	268	97	ν−µ	ν−µ	NOUN
ejpam-6138	268	98	2	2	NUM
ejpam-6138	268	99	»	»	NOUN
ejpam-6138	268	100	»	»	PRON
ejpam-6138	268	101	»	»	PRON
ejpam-6138	268	102	»	»	PRON
ejpam-6138	268	103	»	»	PUNCT
ejpam-6138	268	104	+	+	ADJ
ejpam-6138	268	105	»	»	PUNCT
ejpam-6138	268	106	»	»	PRON
ejpam-6138	268	107	»	»	PUNCT
ejpam-6138	268	108	»	»	PRON
ejpam-6138	268	109	»	»	X
ejpam-6138	268	110	µ	µ	NOUN
ejpam-6138	268	111	′	′	NOUN
ejpam-6138	268	112	−	−	PROPN
ejpam-6138	268	113	ν	ν	NOUN
ejpam-6138	268	114	′	′	NUM
ejpam-6138	268	115	»	»	PUNCT
ejpam-6138	268	116	»	»	PUNCT
ejpam-6138	268	117	»	»	PRON
ejpam-6138	268	118	»	»	ADV
ejpam-6138	268	119	»	»	X
ejpam-6138	268	120	≤	≤	X
ejpam-6138	268	121	ζ∣µ	ζ∣µ	PUNCT
ejpam-6138	268	122	−	−	PROPN
ejpam-6138	268	123	ν∣	ν∣	NOUN
ejpam-6138	268	124	+	+	PUNCT
ejpam-6138	268	125	η∣µ′	η∣µ′	NOUN
ejpam-6138	268	126	−	−	NOUN
ejpam-6138	268	127	ν	ν	NOUN
ejpam-6138	268	128	′∣	′∣	PROPN
ejpam-6138	268	129	,	,	PUNCT
ejpam-6138	268	130	for	for	ADP
ejpam-6138	268	131	(	(	PUNCT
ejpam-6138	268	132	τ	τ	PROPN
ejpam-6138	268	133	,	,	PUNCT
ejpam-6138	268	134	µ	µ	NOUN
ejpam-6138	268	135	,	,	PUNCT
ejpam-6138	268	136	µ′	µ′	NOUN
ejpam-6138	268	137	)	)	PUNCT
ejpam-6138	268	138	,	,	PUNCT
ejpam-6138	268	139	(	(	PUNCT
ejpam-6138	268	140	τ	τ	X
ejpam-6138	268	141	,	,	PUNCT
ejpam-6138	268	142	ν	ν	PROPN
ejpam-6138	268	143	,	,	PUNCT
ejpam-6138	268	144	ν	ν	NOUN
ejpam-6138	268	145	′	′	NOUN
ejpam-6138	268	146	)	)	PUNCT
ejpam-6138	268	147	∈	∈	PROPN
ejpam-6138	269	1	[	[	X
ejpam-6138	269	2	0	0	NUM
ejpam-6138	269	3	,	,	PUNCT
ejpam-6138	269	4	1	1	NUM
ejpam-6138	269	5	]	]	SYM
ejpam-6138	269	6	×	×	NOUN
ejpam-6138	269	7	r2	r2	NOUN
ejpam-6138	269	8	,	,	PUNCT
ejpam-6138	269	9	where	where	SCONJ
ejpam-6138	269	10	η	η	PROPN
ejpam-6138	269	11	=	=	PROPN
ejpam-6138	269	12	1	1	NUM
ejpam-6138	269	13	≥	≥	NOUN
ejpam-6138	269	14	0	0	NUM
ejpam-6138	269	15	,	,	PUNCT
ejpam-6138	269	16	ζ	ζ	NOUN
ejpam-6138	269	17	=	=	SYM
ejpam-6138	269	18	1	1	NUM
ejpam-6138	269	19	>	>	X
ejpam-6138	269	20	0	0	X
ejpam-6138	269	21	.	.	PUNCT
ejpam-6138	270	1	moreover	moreover	ADV
ejpam-6138	270	2	,	,	PUNCT
ejpam-6138	270	3	we	we	PRON
ejpam-6138	270	4	have	have	VERB
ejpam-6138	270	5	ϖ	ϖ	NOUN
ejpam-6138	270	6	=	=	SYM
ejpam-6138	270	7	ζ	ζ	NOUN
ejpam-6138	270	8	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-6138	270	9	)	)	PUNCT
ejpam-6138	270	10	[	[	PUNCT
ejpam-6138	270	11	1	1	NUM
ejpam-6138	270	12	σ1/(σ−1	σ1/(σ−1	NOUN
ejpam-6138	270	13	)	)	PUNCT
ejpam-6138	270	14	−	−	PROPN
ejpam-6138	270	15	1	1	NUM
ejpam-6138	270	16	σσ/(σ−1	σσ/(σ−1	NUM
ejpam-6138	270	17	)	)	PUNCT
ejpam-6138	270	18	]	]	PUNCT
ejpam-6138	271	1	+	+	CCONJ
ejpam-6138	271	2	η	η	PROPN
ejpam-6138	271	3	ϱσ−1γ(σ+1	ϱσ−1γ(σ+1	PROPN
ejpam-6138	271	4	)	)	PUNCT
ejpam-6138	272	1	[	[	X
ejpam-6138	272	2	(	(	PUNCT
ejpam-6138	272	3	ϱ−1	ϱ−1	PROPN
ejpam-6138	272	4	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	272	5	)	)	PUNCT
ejpam-6138	272	6	)	)	PUNCT
ejpam-6138	272	7	(	(	PUNCT
ejpam-6138	272	8	ϱ−1)/ϱ(σ−1	ϱ−1)/ϱ(σ−1	NOUN
ejpam-6138	272	9	)	)	PUNCT
ejpam-6138	272	10	−σ	−σ	NOUN
ejpam-6138	272	11	(	(	PUNCT
ejpam-6138	272	12	ϱ−1	ϱ−1	PROPN
ejpam-6138	272	13	σ(ϱσ−1	σ(ϱσ−1	PROPN
ejpam-6138	272	14	)	)	PUNCT
ejpam-6138	272	15	)	)	PUNCT
ejpam-6138	272	16	(	(	PUNCT
ejpam-6138	272	17	ϱσ−1)/ϱ(σ−1	ϱσ−1)/ϱ(σ−1	X
ejpam-6138	272	18	)	)	PUNCT
ejpam-6138	272	19	]	]	PUNCT
ejpam-6138	273	1	≈	≈	PROPN
ejpam-6138	273	2	⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩	⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩	PROPN
ejpam-6138	273	3	0.9285	0.9285	NUM
ejpam-6138	273	4	,	,	PUNCT
ejpam-6138	273	5	σ	σ	X
ejpam-6138	273	6	=	=	SYM
ejpam-6138	273	7	4	4	NUM
ejpam-6138	273	8	3	3	NUM
ejpam-6138	273	9	,	,	PUNCT
ejpam-6138	273	10	0.3989	0.3989	NUM
ejpam-6138	273	11	,	,	PUNCT
ejpam-6138	273	12	σ	σ	NOUN
ejpam-6138	273	13	=	=	SYM
ejpam-6138	273	14	3	3	NUM
ejpam-6138	273	15	2	2	NUM
ejpam-6138	273	16	,	,	PUNCT
ejpam-6138	273	17	0.7481	0.7481	NUM
ejpam-6138	273	18	,	,	PUNCT
ejpam-6138	273	19	σ	σ	NOUN
ejpam-6138	273	20	=	=	NOUN
ejpam-6138	273	21	7	7	NUM
ejpam-6138	273	22	4	4	NUM
ejpam-6138	273	23	,	,	PUNCT
ejpam-6138	273	24	⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭	⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭	X
ejpam-6138	273	25	<	<	X
ejpam-6138	273	26	1	1	X
ejpam-6138	273	27	.	.	PUNCT
ejpam-6138	274	1	in	in	ADP
ejpam-6138	274	2	the	the	DET
ejpam-6138	274	3	last	last	ADJ
ejpam-6138	274	4	row	row	NOUN
ejpam-6138	274	5	of	of	ADP
ejpam-6138	274	6	data	datum	NOUN
ejpam-6138	274	7	in	in	ADP
ejpam-6138	274	8	table	table	NOUN
ejpam-6138	274	9	2	2	NUM
ejpam-6138	274	10	,	,	PUNCT
ejpam-6138	274	11	the	the	DET
ejpam-6138	274	12	values	value	NOUN
ejpam-6138	274	13	of	of	ADP
ejpam-6138	274	14	parameter	parameter	PROPN
ejpam-6138	274	15	ϖ	ϖ	PROPN
ejpam-6138	274	16	,	,	PUNCT
ejpam-6138	274	17	at	at	ADP
ejpam-6138	274	18	point	point	NOUN
ejpam-6138	274	19	ϑ	ϑ	VERB
ejpam-6138	274	20	,	,	PUNCT
ejpam-6138	274	21	for	for	ADP
ejpam-6138	274	22	three	three	NUM
ejpam-6138	274	23	different	different	ADJ
ejpam-6138	274	24	values	value	NOUN
ejpam-6138	274	25	of	of	ADP
ejpam-6138	274	26	derivative	derivative	ADJ
ejpam-6138	274	27	order	order	NOUN
ejpam-6138	274	28	σ	σ	NOUN
ejpam-6138	274	29	are	be	AUX
ejpam-6138	274	30	shown	show	VERB
ejpam-6138	274	31	.	.	PUNCT
ejpam-6138	275	1	the	the	DET
ejpam-6138	275	2	curves	curve	NOUN
ejpam-6138	275	3	of	of	ADP
ejpam-6138	275	4	all	all	DET
ejpam-6138	275	5	three	three	NUM
ejpam-6138	275	6	cases	case	NOUN
ejpam-6138	275	7	are	be	AUX
ejpam-6138	275	8	presented	present	VERB
ejpam-6138	275	9	in	in	ADP
ejpam-6138	275	10	figure	figure	NOUN
ejpam-6138	275	11	2	2	NUM
ejpam-6138	275	12	,	,	PUNCT
ejpam-6138	275	13	which	which	PRON
ejpam-6138	275	14	are	be	AUX
ejpam-6138	275	15	decreasing	decrease	VERB
ejpam-6138	275	16	as	as	ADP
ejpam-6138	275	17	the	the	DET
ejpam-6138	275	18	order	order	NOUN
ejpam-6138	275	19	of	of	ADP
ejpam-6138	275	20	the	the	DET
ejpam-6138	275	21	derivative	derivative	ADJ
ejpam-6138	275	22	increases	increase	NOUN
ejpam-6138	275	23	and	and	CCONJ
ejpam-6138	275	24	in	in	ADP
ejpam-6138	275	25	all	all	DET
ejpam-6138	275	26	cases	case	NOUN
ejpam-6138	275	27	are	be	AUX
ejpam-6138	275	28	less	less	ADJ
ejpam-6138	275	29	than	than	ADP
ejpam-6138	275	30	the	the	DET
ejpam-6138	275	31	y	y	NOUN
ejpam-6138	275	32	=	=	SYM
ejpam-6138	275	33	1	1	NUM
ejpam-6138	275	34	line	line	NOUN
ejpam-6138	275	35	.	.	PUNCT
ejpam-6138	276	1	by	by	ADP
ejpam-6138	276	2	the	the	DET
ejpam-6138	276	3	applications	application	NOUN
ejpam-6138	276	4	of	of	ADP
ejpam-6138	276	5	theorem	theorem	NOUN
ejpam-6138	276	6	3	3	NUM
ejpam-6138	276	7	,	,	PUNCT
ejpam-6138	276	8	and	and	CCONJ
ejpam-6138	276	9	the	the	DET
ejpam-6138	276	10	condition	condition	NOUN
ejpam-6138	276	11	(	(	PUNCT
ejpam-6138	276	12	3.19	3.19	NUM
ejpam-6138	276	13	)	)	PUNCT
ejpam-6138	276	14	is	be	AUX
ejpam-6138	276	15	agreed	agree	VERB
ejpam-6138	276	16	.	.	PUNCT
ejpam-6138	277	1	then	then	ADV
ejpam-6138	277	2	the	the	DET
ejpam-6138	277	3	bvp	bvp	PROPN
ejpam-6138	277	4	(	(	PUNCT
ejpam-6138	277	5	4.2	4.2	NUM
ejpam-6138	277	6	)	)	PUNCT
ejpam-6138	277	7	accepts	accept	VERB
ejpam-6138	277	8	an	an	DET
ejpam-6138	277	9	unique	unique	ADJ
ejpam-6138	277	10	solution	solution	NOUN
ejpam-6138	277	11	.	.	PUNCT
ejpam-6138	278	1	z.	z.	PROPN
ejpam-6138	278	2	bekri	bekri	PROPN
ejpam-6138	278	3	et	et	PROPN
ejpam-6138	278	4	al	al	PROPN
ejpam-6138	278	5	.	.	PUNCT
ejpam-6138	278	6	/	/	SYM
ejpam-6138	278	7	eur	eur	PROPN
ejpam-6138	278	8	.	.	PUNCT
ejpam-6138	279	1	j.	j.	PROPN
ejpam-6138	279	2	pure	pure	PROPN
ejpam-6138	279	3	appl	appl	PROPN
ejpam-6138	279	4	.	.	PROPN
ejpam-6138	279	5	math	math	PROPN
ejpam-6138	279	6	,	,	PUNCT
ejpam-6138	279	7	18	18	NUM
ejpam-6138	279	8	(	(	PUNCT
ejpam-6138	279	9	2	2	NUM
ejpam-6138	279	10	)	)	PUNCT
ejpam-6138	279	11	(	(	PUNCT
ejpam-6138	279	12	2025	2025	NUM
ejpam-6138	279	13	)	)	PUNCT
ejpam-6138	279	14	,	,	PUNCT
ejpam-6138	279	15	6138	6138	NUM
ejpam-6138	279	16	14	14	NUM
ejpam-6138	279	17	of	of	ADP
ejpam-6138	279	18	17	17	NUM
ejpam-6138	279	19	table	table	NOUN
ejpam-6138	279	20	2	2	NUM
ejpam-6138	279	21	:	:	PUNCT
ejpam-6138	279	22	numerical	numerical	ADJ
ejpam-6138	279	23	results	result	NOUN
ejpam-6138	279	24	ϖ	ϖ	VERB
ejpam-6138	279	25	in	in	ADP
ejpam-6138	279	26	example	example	NOUN
ejpam-6138	279	27	2	2	NUM
ejpam-6138	279	28	for	for	ADP
ejpam-6138	279	29	three	three	NUM
ejpam-6138	279	30	values	value	NOUN
ejpam-6138	279	31	of	of	ADP
ejpam-6138	279	32	σ	σ	PROPN
ejpam-6138	279	33	.	.	PUNCT
ejpam-6138	280	1	τ	τ	PROPN
ejpam-6138	280	2	ϖ	ϖ	PROPN
ejpam-6138	280	3	σ	σ	NOUN
ejpam-6138	280	4	=	=	SYM
ejpam-6138	280	5	4	4	NUM
ejpam-6138	280	6	3	3	NUM
ejpam-6138	280	7	σ	σ	NOUN
ejpam-6138	280	8	=	=	SYM
ejpam-6138	280	9	4	4	NUM
ejpam-6138	280	10	3	3	NUM
ejpam-6138	280	11	σ	σ	NOUN
ejpam-6138	280	12	=	=	SYM
ejpam-6138	280	13	4	4	NUM
ejpam-6138	280	14	3	3	NUM
ejpam-6138	280	15	σ	σ	NOUN
ejpam-6138	280	16	=	=	SYM
ejpam-6138	280	17	5	5	NUM
ejpam-6138	280	18	2	2	NUM
ejpam-6138	280	19	σ	σ	NOUN
ejpam-6138	280	20	=	=	SYM
ejpam-6138	280	21	5	5	NUM
ejpam-6138	280	22	2	2	NUM
ejpam-6138	280	23	σ	σ	NOUN
ejpam-6138	280	24	=	=	SYM
ejpam-6138	280	25	5	5	NUM
ejpam-6138	280	26	2	2	NUM
ejpam-6138	280	27	σ	σ	NOUN
ejpam-6138	280	28	=	=	NOUN
ejpam-6138	280	29	7	7	NUM
ejpam-6138	280	30	4	4	NUM
ejpam-6138	280	31	σ	σ	NOUN
ejpam-6138	280	32	=	=	NOUN
ejpam-6138	280	33	7	7	NUM
ejpam-6138	280	34	4	4	NUM
ejpam-6138	280	35	σ	σ	NOUN
ejpam-6138	280	36	=	=	NOUN
ejpam-6138	280	37	7	7	NUM
ejpam-6138	280	38	4	4	NUM
ejpam-6138	280	39	0.00	0.00	NUM
ejpam-6138	280	40	0.0000	0.0000	NUM
ejpam-6138	280	41	0.0000	0.0000	NUM
ejpam-6138	280	42	0.0000	0.0000	NUM
ejpam-6138	280	43	0.05	0.05	NUM
ejpam-6138	280	44	0.3110	0.3110	NUM
ejpam-6138	280	45	0.1695	0.1695	NUM
ejpam-6138	280	46	0.0664	0.0664	NUM
ejpam-6138	280	47	0.10	0.10	NUM
ejpam-6138	280	48	0.3940	0.3940	NUM
ejpam-6138	280	49	0.2414	0.2414	NUM
ejpam-6138	280	50	0.1128	0.1128	NUM
ejpam-6138	280	51	0.15	0.15	NUM
ejpam-6138	280	52	0.4533	0.4533	NUM
ejpam-6138	280	53	0.2978	0.2978	NUM
ejpam-6138	280	54	0.1544	0.1544	NUM
ejpam-6138	280	55	0.20	0.20	NUM
ejpam-6138	280	56	0.5015	0.5015	NUM
ejpam-6138	280	57	0.3464	0.3464	NUM
ejpam-6138	280	58	0.1935	0.1935	NUM
ejpam-6138	280	59	0.25	0.25	NUM
ejpam-6138	280	60	0.5430	0.5430	NUM
ejpam-6138	280	61	0.3901	0.3901	NUM
ejpam-6138	280	62	0.2310	0.2310	NUM
ejpam-6138	280	63	0.30	0.30	NUM
ejpam-6138	280	64	0.5800	0.5800	NUM
ejpam-6138	280	65	0.4303	0.4303	NUM
ejpam-6138	280	66	0.2674	0.2674	NUM
ejpam-6138	280	67	0.35	0.35	NUM
ejpam-6138	280	68	0.6137	0.6137	NUM
ejpam-6138	280	69	0.4681	0.4681	NUM
ejpam-6138	280	70	0.3030	0.3030	NUM
ejpam-6138	280	71	0.40	0.40	NUM
ejpam-6138	280	72	0.6449	0.6449	NUM
ejpam-6138	280	73	0.5040	0.5040	NUM
ejpam-6138	280	74	0.3381	0.3381	NUM
ejpam-6138	280	75	0.45	0.45	NUM
ejpam-6138	280	76	0.6742	0.6742	NUM
ejpam-6138	280	77	0.5383	0.5383	NUM
ejpam-6138	280	78	0.3728	0.3728	NUM
ejpam-6138	280	79	0.50	0.50	NUM
ejpam-6138	280	80	0.7018	0.7018	NUM
ejpam-6138	280	81	0.5713	0.5713	NUM
ejpam-6138	281	1	0.4073	0.4073	NUM
ejpam-6138	281	2	0.55	0.55	NUM
ejpam-6138	281	3	0.7281	0.7281	NUM
ejpam-6138	281	4	0.6033	0.6033	NUM
ejpam-6138	281	5	0.4415	0.4415	NUM
ejpam-6138	281	6	0.60	0.60	NUM
ejpam-6138	281	7	0.7532	0.7532	NUM
ejpam-6138	281	8	0.6345	0.6345	NUM
ejpam-6138	281	9	0.4756	0.4756	NUM
ejpam-6138	281	10	0.65	0.65	NUM
ejpam-6138	281	11	0.7774	0.7774	NUM
ejpam-6138	281	12	0.6649	0.6649	NUM
ejpam-6138	281	13	0.5095	0.5095	NUM
ejpam-6138	281	14	0.70	0.70	NUM
ejpam-6138	281	15	0.8008	0.8008	NUM
ejpam-6138	281	16	0.6946	0.6946	NUM
ejpam-6138	281	17	0.5435	0.5435	NUM
ejpam-6138	281	18	0.75	0.75	NUM
ejpam-6138	281	19	0.8234	0.8234	NUM
ejpam-6138	281	20	0.7239	0.7239	NUM
ejpam-6138	281	21	0.5775	0.5775	NUM
ejpam-6138	281	22	0.80	0.80	NUM
ejpam-6138	281	23	0.8455	0.8455	NUM
ejpam-6138	281	24	0.7526	0.7526	NUM
ejpam-6138	281	25	0.6114	0.6114	NUM
ejpam-6138	281	26	0.85	0.85	NUM
ejpam-6138	281	27	0.8669	0.8669	NUM
ejpam-6138	281	28	0.7809	0.7809	NUM
ejpam-6138	281	29	0.6455	0.6455	NUM
ejpam-6138	281	30	0.90	0.90	NUM
ejpam-6138	281	31	0.8879	0.8879	NUM
ejpam-6138	281	32	0.8088	0.8088	NUM
ejpam-6138	281	33	0.6796	0.6796	NUM
ejpam-6138	281	34	0.95	0.95	NUM
ejpam-6138	281	35	0.9084	0.9084	NUM
ejpam-6138	281	36	0.8364	0.8364	NUM
ejpam-6138	281	37	0.7138	0.7138	NUM
ejpam-6138	281	38	1.00	1.00	NUM
ejpam-6138	281	39	0.9285	0.9285	NUM
ejpam-6138	281	40	0.8637	0.8637	NUM
ejpam-6138	281	41	0.7481	0.7481	NUM
ejpam-6138	281	42	τ	τ	X
ejpam-6138	281	43	0	0	NUM
ejpam-6138	281	44	0.1	0.1	NUM
ejpam-6138	281	45	0.2	0.2	NUM
ejpam-6138	281	46	0.3	0.3	NUM
ejpam-6138	281	47	0.4	0.4	NUM
ejpam-6138	281	48	0.5	0.5	NUM
ejpam-6138	281	49	0.6	0.6	NUM
ejpam-6138	281	50	0.7	0.7	NUM
ejpam-6138	281	51	0.8	0.8	NUM
ejpam-6138	281	52	0.9	0.9	NUM
ejpam-6138	281	53	1	1	NUM
ejpam-6138	281	54	̟	̟	PROPN
ejpam-6138	281	55	0	0	NUM
ejpam-6138	281	56	0.1	0.1	NUM
ejpam-6138	281	57	0.2	0.2	NUM
ejpam-6138	281	58	0.3	0.3	NUM
ejpam-6138	281	59	0.4	0.4	NUM
ejpam-6138	281	60	0.5	0.5	NUM
ejpam-6138	281	61	0.6	0.6	NUM
ejpam-6138	281	62	0.7	0.7	NUM
ejpam-6138	281	63	0.8	0.8	NUM
ejpam-6138	281	64	0.9	0.9	NUM
ejpam-6138	281	65	1	1	NUM
ejpam-6138	281	66	̟	̟	PRON
ejpam-6138	281	67	<	<	X
ejpam-6138	281	68	1	1	NUM
ejpam-6138	281	69	σ=4/3	σ=4/3	PROPN
ejpam-6138	281	70	σ=3/2	σ=3/2	NOUN
ejpam-6138	281	71	σ=7/4	σ=7/4	PROPN
ejpam-6138	281	72	figure	figure	NOUN
ejpam-6138	281	73	2	2	NUM
ejpam-6138	281	74	:	:	PUNCT
ejpam-6138	281	75	representation	representation	NOUN
ejpam-6138	281	76	of	of	ADP
ejpam-6138	281	77	ϖ	ϖ	PROPN
ejpam-6138	281	78	for	for	ADP
ejpam-6138	281	79	bvp	bvp	NOUN
ejpam-6138	281	80	(	(	PUNCT
ejpam-6138	281	81	4.2	4.2	NUM
ejpam-6138	281	82	)	)	PUNCT
ejpam-6138	281	83	in	in	ADP
ejpam-6138	281	84	example	example	NOUN
ejpam-6138	281	85	2	2	NUM
ejpam-6138	281	86	for	for	ADP
ejpam-6138	281	87	three	three	NUM
ejpam-6138	281	88	case	case	NOUN
ejpam-6138	281	89	σ	σ	X
ejpam-6138	281	90	.	.	PROPN
ejpam-6138	281	91	5	5	NUM
ejpam-6138	281	92	.	.	PUNCT
ejpam-6138	281	93	conclusions	conclusion	NOUN
ejpam-6138	281	94	through	through	ADP
ejpam-6138	281	95	this	this	DET
ejpam-6138	281	96	project	project	NOUN
ejpam-6138	281	97	,	,	PUNCT
ejpam-6138	281	98	we	we	PRON
ejpam-6138	281	99	tried	try	VERB
ejpam-6138	281	100	to	to	PART
ejpam-6138	281	101	simulate	simulate	VERB
ejpam-6138	281	102	the	the	DET
ejpam-6138	281	103	banach	banach	NOUN
ejpam-6138	281	104	contraction	contraction	NOUN
ejpam-6138	281	105	theorem	theorem	VERB
ejpam-6138	281	106	on	on	ADP
ejpam-6138	281	107	the	the	DET
ejpam-6138	281	108	caputo	caputo	PROPN
ejpam-6138	281	109	-	-	PUNCT
ejpam-6138	281	110	katugampola	katugampola	PROPN
ejpam-6138	281	111	fractional	fractional	ADJ
ejpam-6138	281	112	derivative	derivative	ADJ
ejpam-6138	281	113	boundary	boundary	ADJ
ejpam-6138	281	114	value	value	NOUN
ejpam-6138	281	115	problem	problem	NOUN
ejpam-6138	281	116	to	to	PART
ejpam-6138	281	117	achieve	achieve	VERB
ejpam-6138	281	118	the	the	DET
ejpam-6138	281	119	existence	existence	NOUN
ejpam-6138	281	120	of	of	ADP
ejpam-6138	281	121	a	a	DET
ejpam-6138	281	122	single	single	ADJ
ejpam-6138	281	123	solution	solution	NOUN
ejpam-6138	281	124	,	,	PUNCT
ejpam-6138	281	125	the	the	DET
ejpam-6138	281	126	core	core	NOUN
ejpam-6138	281	127	of	of	ADP
ejpam-6138	281	128	this	this	DET
ejpam-6138	281	129	work	work	NOUN
ejpam-6138	281	130	in	in	ADP
ejpam-6138	281	131	the	the	DET
ejpam-6138	281	132	third	third	ADJ
ejpam-6138	281	133	chapter	chapter	NOUN
ejpam-6138	281	134	.	.	PUNCT
ejpam-6138	282	1	we	we	PRON
ejpam-6138	282	2	relied	rely	VERB
ejpam-6138	282	3	on	on	ADP
ejpam-6138	282	4	the	the	DET
ejpam-6138	282	5	z.	z.	PROPN
ejpam-6138	282	6	bekri	bekri	PROPN
ejpam-6138	282	7	et	et	PROPN
ejpam-6138	282	8	al	al	PROPN
ejpam-6138	282	9	.	.	PUNCT
ejpam-6138	282	10	/	/	SYM
ejpam-6138	282	11	eur	eur	PROPN
ejpam-6138	282	12	.	.	PUNCT
ejpam-6138	283	1	j.	j.	PROPN
ejpam-6138	283	2	pure	pure	PROPN
ejpam-6138	283	3	appl	appl	PROPN
ejpam-6138	283	4	.	.	PROPN
ejpam-6138	283	5	math	math	PROPN
ejpam-6138	283	6	,	,	PUNCT
ejpam-6138	283	7	18	18	NUM
ejpam-6138	283	8	(	(	PUNCT
ejpam-6138	283	9	2	2	NUM
ejpam-6138	283	10	)	)	PUNCT
ejpam-6138	283	11	(	(	PUNCT
ejpam-6138	283	12	2025	2025	NUM
ejpam-6138	283	13	)	)	PUNCT
ejpam-6138	283	14	,	,	PUNCT
ejpam-6138	283	15	6138	6138	NUM
ejpam-6138	283	16	15	15	NUM
ejpam-6138	283	17	of	of	ADP
ejpam-6138	283	18	17	17	NUM
ejpam-6138	283	19	positivity	positivity	NOUN
ejpam-6138	283	20	of	of	ADP
ejpam-6138	283	21	the	the	DET
ejpam-6138	283	22	green	green	ADJ
ejpam-6138	283	23	function	function	NOUN
ejpam-6138	283	24	and	and	CCONJ
ejpam-6138	283	25	its	its	PRON
ejpam-6138	283	26	integral	integral	ADJ
ejpam-6138	283	27	and	and	CCONJ
ejpam-6138	283	28	obtained	obtain	VERB
ejpam-6138	283	29	the	the	DET
ejpam-6138	283	30	two	two	NUM
ejpam-6138	283	31	functions	function	NOUN
ejpam-6138	283	32	ξ	ξ	PROPN
ejpam-6138	283	33	and	and	CCONJ
ejpam-6138	283	34	ξ	ξ	X
ejpam-6138	283	35	′	′	NOUN
ejpam-6138	283	36	as	as	SCONJ
ejpam-6138	283	37	shown	show	VERB
ejpam-6138	283	38	in	in	ADP
ejpam-6138	283	39	corollary	corollary	ADJ
ejpam-6138	283	40	1	1	NUM
ejpam-6138	283	41	.	.	PUNCT
ejpam-6138	284	1	by	by	ADP
ejpam-6138	284	2	conclusion	conclusion	NOUN
ejpam-6138	284	3	,	,	PUNCT
ejpam-6138	284	4	we	we	PRON
ejpam-6138	284	5	can	can	AUX
ejpam-6138	284	6	determine	determine	VERB
ejpam-6138	284	7	the	the	DET
ejpam-6138	284	8	maximum	maximum	NOUN
ejpam-6138	284	9	of	of	ADP
ejpam-6138	284	10	two	two	NUM
ejpam-6138	284	11	derived	derive	VERB
ejpam-6138	284	12	functions	function	NOUN
ejpam-6138	284	13	in	in	ADP
ejpam-6138	284	14	the	the	DET
ejpam-6138	284	15	general	general	ADJ
ejpam-6138	284	16	case	case	NOUN
ejpam-6138	284	17	of	of	ADP
ejpam-6138	284	18	two	two	NUM
ejpam-6138	284	19	boundary	boundary	ADJ
ejpam-6138	284	20	conditions	condition	NOUN
ejpam-6138	284	21	“	"	PUNCT
ejpam-6138	284	22	µ(θ	µ(θ	ADJ
ejpam-6138	284	23	)	)	PUNCT
ejpam-6138	284	24	=	=	SYM
ejpam-6138	284	25	λ1	λ1	ADJ
ejpam-6138	284	26	,	,	PUNCT
ejpam-6138	284	27	µ(ϑ	µ(ϑ	PROPN
ejpam-6138	284	28	)	)	PUNCT
ejpam-6138	284	29	=	=	SYM
ejpam-6138	284	30	λ2	λ2	NOUN
ejpam-6138	284	31	”	"	PUNCT
ejpam-6138	284	32	.	.	PUNCT
ejpam-6138	285	1	we	we	PRON
ejpam-6138	285	2	studied	study	VERB
ejpam-6138	285	3	two	two	NUM
ejpam-6138	285	4	cases	case	NOUN
ejpam-6138	285	5	when	when	SCONJ
ejpam-6138	285	6	“	"	PUNCT
ejpam-6138	285	7	µ(0	µ(0	NOUN
ejpam-6138	285	8	)	)	PUNCT
ejpam-6138	285	9	=	=	SYM
ejpam-6138	285	10	λ1	λ1	ADJ
ejpam-6138	285	11	,	,	PUNCT
ejpam-6138	285	12	µ(ϑ	µ(ϑ	PROPN
ejpam-6138	285	13	)	)	PUNCT
ejpam-6138	285	14	=	=	SYM
ejpam-6138	285	15	λ2	λ2	NOUN
ejpam-6138	285	16	”	"	PUNCT
ejpam-6138	285	17	and	and	CCONJ
ejpam-6138	285	18	“	"	PUNCT
ejpam-6138	285	19	µ(0	µ(0	NOUN
ejpam-6138	285	20	)	)	PUNCT
ejpam-6138	285	21	=	=	SYM
ejpam-6138	285	22	λ1	λ1	PROPN
ejpam-6138	285	23	,	,	PUNCT
ejpam-6138	285	24	µ(1	µ(1	PROPN
ejpam-6138	285	25	)	)	PUNCT
ejpam-6138	285	26	=	=	SYM
ejpam-6138	285	27	λ2	λ2	PROPN
ejpam-6138	285	28	”	"	PUNCT
ejpam-6138	285	29	in	in	ADP
ejpam-6138	285	30	theorems	theorem	NOUN
ejpam-6138	285	31	2	2	NUM
ejpam-6138	285	32	and	and	CCONJ
ejpam-6138	285	33	3	3	NUM
ejpam-6138	285	34	,	,	PUNCT
ejpam-6138	285	35	we	we	PRON
ejpam-6138	285	36	obtain	obtain	VERB
ejpam-6138	285	37	detailed	detailed	ADJ
ejpam-6138	285	38	results	result	NOUN
ejpam-6138	285	39	in	in	ADP
ejpam-6138	285	40	this	this	DET
ejpam-6138	285	41	section	section	NOUN
ejpam-6138	285	42	.	.	PUNCT
ejpam-6138	286	1	we	we	PRON
ejpam-6138	286	2	also	also	ADV
ejpam-6138	286	3	studied	study	VERB
ejpam-6138	286	4	two	two	NUM
ejpam-6138	286	5	cases	case	NOUN
ejpam-6138	286	6	when	when	SCONJ
ejpam-6138	286	7	,	,	PUNCT
ejpam-6138	286	8	the	the	DET
ejpam-6138	286	9	previous	previous	ADJ
ejpam-6138	286	10	general	general	ADJ
ejpam-6138	286	11	case	case	NOUN
ejpam-6138	286	12	“	"	PUNCT
ejpam-6138	286	13	µ(θ	µ(θ	ADJ
ejpam-6138	286	14	)	)	PUNCT
ejpam-6138	286	15	=	=	SYM
ejpam-6138	286	16	λ1	λ1	ADJ
ejpam-6138	286	17	,	,	PUNCT
ejpam-6138	286	18	µ(ϑ	µ(ϑ	PROPN
ejpam-6138	286	19	)	)	PUNCT
ejpam-6138	286	20	=	=	SYM
ejpam-6138	286	21	λ2	λ2	NOUN
ejpam-6138	286	22	”	"	PUNCT
ejpam-6138	286	23	and	and	CCONJ
ejpam-6138	286	24	the	the	DET
ejpam-6138	286	25	case	case	NOUN
ejpam-6138	286	26	of	of	ADP
ejpam-6138	286	27	“	"	PUNCT
ejpam-6138	286	28	µ(θ	µ(θ	ADJ
ejpam-6138	286	29	)	)	PUNCT
ejpam-6138	286	30	=	=	SYM
ejpam-6138	286	31	λ1	λ1	PROPN
ejpam-6138	286	32	,	,	PUNCT
ejpam-6138	286	33	µ(1	µ(1	PROPN
ejpam-6138	286	34	)	)	PUNCT
ejpam-6138	286	35	=	=	SYM
ejpam-6138	286	36	λ2	λ2	PROPN
ejpam-6138	286	37	”	"	PUNCT
ejpam-6138	286	38	,	,	PUNCT
ejpam-6138	286	39	we	we	PRON
ejpam-6138	286	40	can	can	AUX
ejpam-6138	286	41	also	also	ADV
ejpam-6138	286	42	add	add	VERB
ejpam-6138	286	43	two	two	NUM
ejpam-6138	286	44	examples	example	NOUN
ejpam-6138	286	45	with	with	ADP
ejpam-6138	286	46	their	their	PRON
ejpam-6138	286	47	simulation	simulation	NOUN
ejpam-6138	286	48	in	in	ADP
ejpam-6138	286	49	these	these	DET
ejpam-6138	286	50	two	two	NUM
ejpam-6138	286	51	cases	case	NOUN
ejpam-6138	286	52	of	of	ADP
ejpam-6138	286	53	theorems	theorem	NOUN
ejpam-6138	286	54	4	4	NUM
ejpam-6138	286	55	and	and	CCONJ
ejpam-6138	286	56	5	5	NUM
ejpam-6138	286	57	in	in	ADP
ejpam-6138	286	58	the	the	DET
ejpam-6138	286	59	examples	example	NOUN
ejpam-6138	286	60	part	part	NOUN
ejpam-6138	286	61	.	.	PUNCT
ejpam-6138	287	1	we	we	PRON
ejpam-6138	287	2	also	also	ADV
ejpam-6138	287	3	believe	believe	VERB
ejpam-6138	287	4	there	there	PRON
ejpam-6138	287	5	are	be	VERB
ejpam-6138	287	6	numerical	numerical	ADJ
ejpam-6138	287	7	methods	method	NOUN
ejpam-6138	287	8	to	to	PART
ejpam-6138	287	9	achieve	achieve	VERB
ejpam-6138	287	10	banach	banach	NOUN
ejpam-6138	287	11	’s	’s	NOUN
ejpam-6138	287	12	theorem	theorem	NOUN
ejpam-6138	287	13	of	of	ADP
ejpam-6138	287	14	contraction	contraction	NOUN
ejpam-6138	287	15	of	of	ADP
ejpam-6138	287	16	a	a	DET
ejpam-6138	287	17	single	single	ADJ
ejpam-6138	287	18	solution	solution	NOUN
ejpam-6138	287	19	to	to	ADP
ejpam-6138	287	20	the	the	DET
ejpam-6138	287	21	problem	problem	NOUN
ejpam-6138	287	22	(	(	PUNCT
ejpam-6138	287	23	1.4	1.4	NUM
ejpam-6138	287	24	)	)	PUNCT
ejpam-6138	287	25	with	with	ADP
ejpam-6138	287	26	the	the	DET
ejpam-6138	287	27	general	general	ADJ
ejpam-6138	287	28	boundary	boundary	ADJ
ejpam-6138	287	29	conditions	condition	NOUN
ejpam-6138	287	30	.	.	PUNCT
ejpam-6138	288	1	in	in	ADP
ejpam-6138	288	2	the	the	DET
ejpam-6138	288	3	future	future	NOUN
ejpam-6138	288	4	,	,	PUNCT
ejpam-6138	288	5	we	we	PRON
ejpam-6138	288	6	can	can	AUX
ejpam-6138	288	7	apply	apply	VERB
ejpam-6138	288	8	the	the	DET
ejpam-6138	288	9	banach	banach	NOUN
ejpam-6138	288	10	contraction	contraction	NOUN
ejpam-6138	288	11	to	to	ADP
ejpam-6138	288	12	the	the	DET
ejpam-6138	288	13	caputo	caputo	PROPN
ejpam-6138	288	14	-	-	PUNCT
ejpam-6138	288	15	fabrizio	fabrizio	PROPN
ejpam-6138	288	16	fractional	fractional	PROPN
ejpam-6138	288	17	bvp	bvp	NOUN
ejpam-6138	288	18	.	.	PUNCT
ejpam-6138	289	1	acknowledgements	acknowledgement	NOUN
ejpam-6138	289	2	the	the	DET
ejpam-6138	289	3	authors	author	NOUN
ejpam-6138	289	4	s.	s.	PROPN
ejpam-6138	289	5	haque	haque	PROPN
ejpam-6138	289	6	and	and	CCONJ
ejpam-6138	289	7	n.	n.	PROPN
ejpam-6138	289	8	mlaiki	mlaiki	PROPN
ejpam-6138	289	9	would	would	AUX
ejpam-6138	289	10	like	like	VERB
ejpam-6138	289	11	to	to	PART
ejpam-6138	289	12	thank	thank	VERB
ejpam-6138	289	13	prince	prince	PROPN
ejpam-6138	289	14	sultan	sultan	PROPN
ejpam-6138	289	15	university	university	PROPN
ejpam-6138	289	16	for	for	ADP
ejpam-6138	289	17	paying	pay	VERB
ejpam-6138	289	18	the	the	DET
ejpam-6138	289	19	apc	apc	NOUN
ejpam-6138	289	20	and	and	CCONJ
ejpam-6138	289	21	for	for	ADP
ejpam-6138	289	22	the	the	DET
ejpam-6138	289	23	support	support	NOUN
ejpam-6138	289	24	through	through	ADP
ejpam-6138	289	25	the	the	DET
ejpam-6138	289	26	tas	tas	PROPN
ejpam-6138	289	27	research	research	NOUN
ejpam-6138	289	28	lab	lab	NOUN
ejpam-6138	289	29	.	.	PUNCT
ejpam-6138	290	1	declarations	declaration	NOUN
ejpam-6138	290	2	authors	author	NOUN
ejpam-6138	290	3	’	’	PART
ejpam-6138	290	4	contributions	contribution	NOUN
ejpam-6138	290	5	z.b	z.b	PROPN
ejpam-6138	290	6	.	.	PROPN
ejpam-6138	290	7	,	,	PUNCT
ejpam-6138	290	8	m.e.s	m.e.s	PROPN
ejpam-6138	290	9	.	.	PROPN
ejpam-6138	290	10	,	,	PUNCT
ejpam-6138	290	11	v.s.e	v.s.e	PROPN
ejpam-6138	290	12	,	,	PUNCT
ejpam-6138	290	13	s.h	s.h	PROPN
ejpam-6138	290	14	.	.	PROPN
ejpam-6138	290	15	and	and	CCONJ
ejpam-6138	290	16	n.m	n.m	PROPN
ejpam-6138	290	17	.	.	PROPN
ejpam-6138	290	18	wrote	write	VERB
ejpam-6138	290	19	the	the	DET
ejpam-6138	290	20	main	main	ADJ
ejpam-6138	290	21	manuscript	manuscript	NOUN
ejpam-6138	290	22	.	.	PUNCT
ejpam-6138	291	1	all	all	DET
ejpam-6138	291	2	authors	author	NOUN
ejpam-6138	291	3	reviewed	review	VERB
ejpam-6138	291	4	the	the	DET
ejpam-6138	291	5	manuscript	manuscript	NOUN
ejpam-6138	291	6	.	.	PUNCT
ejpam-6138	292	1	conflicts	conflict	NOUN
ejpam-6138	292	2	of	of	ADP
ejpam-6138	292	3	interest	interest	NOUN
ejpam-6138	292	4	the	the	DET
ejpam-6138	292	5	authors	author	NOUN
ejpam-6138	292	6	declare	declare	VERB
ejpam-6138	292	7	no	no	DET
ejpam-6138	292	8	conflict	conflict	NOUN
ejpam-6138	292	9	of	of	ADP
ejpam-6138	292	10	interest	interest	NOUN
ejpam-6138	292	11	.	.	PUNCT
ejpam-6138	293	1	references	reference	NOUN
ejpam-6138	293	2	[	[	X
ejpam-6138	293	3	1	1	NUM
ejpam-6138	293	4	]	]	PUNCT
ejpam-6138	293	5	k.	k.	PROPN
ejpam-6138	293	6	benia	benia	PROPN
ejpam-6138	293	7	,	,	PUNCT
ejpam-6138	293	8	m.	m.	NOUN
ejpam-6138	293	9	s.	s.	PROPN
ejpam-6138	293	10	souid	souid	PROPN
ejpam-6138	293	11	,	,	PUNCT
ejpam-6138	293	12	f.	f.	PROPN
ejpam-6138	293	13	jarad	jarad	PROPN
ejpam-6138	293	14	,	,	PUNCT
ejpam-6138	293	15	m.	m.	NOUN
ejpam-6138	293	16	a.	a.	NOUN
ejpam-6138	293	17	alqudah	alqudah	PROPN
ejpam-6138	293	18	,	,	PUNCT
ejpam-6138	293	19	and	and	CCONJ
ejpam-6138	293	20	t.	t.	PROPN
ejpam-6138	293	21	abdeljawad	abdeljawad	NOUN
ejpam-6138	293	22	.	.	PUNCT
ejpam-6138	294	1	boundary	boundary	ADJ
ejpam-6138	294	2	value	value	NOUN
ejpam-6138	294	3	problem	problem	NOUN
ejpam-6138	294	4	of	of	ADP
ejpam-6138	294	5	weighted	weight	VERB
ejpam-6138	294	6	fractional	fractional	ADJ
ejpam-6138	294	7	derivative	derivative	NOUN
ejpam-6138	294	8	of	of	ADP
ejpam-6138	294	9	a	a	DET
ejpam-6138	294	10	function	function	NOUN
ejpam-6138	294	11	with	with	ADP
ejpam-6138	294	12	respect	respect	NOUN
ejpam-6138	294	13	to	to	ADP
ejpam-6138	294	14	another	another	DET
ejpam-6138	294	15	function	function	NOUN
ejpam-6138	294	16	of	of	ADP
ejpam-6138	294	17	variable	variable	ADJ
ejpam-6138	294	18	order	order	NOUN
ejpam-6138	294	19	.	.	PUNCT
ejpam-6138	295	1	journal	journal	NOUN
ejpam-6138	295	2	of	of	ADP
ejpam-6138	295	3	inequalities	inequality	NOUN
ejpam-6138	295	4	and	and	CCONJ
ejpam-6138	295	5	applications	application	NOUN
ejpam-6138	295	6	,	,	PUNCT
ejpam-6138	295	7	2023:127	2023:127	NOUN
ejpam-6138	295	8	,	,	PUNCT
ejpam-6138	295	9	2023	2023	NUM
ejpam-6138	295	10	.	.	PUNCT
ejpam-6138	296	1	[	[	X
ejpam-6138	296	2	2	2	NUM
ejpam-6138	296	3	]	]	PUNCT
ejpam-6138	296	4	k.	k.	PROPN
ejpam-6138	296	5	h.	h.	PROPN
ejpam-6138	296	6	khalid	khalid	PROPN
ejpam-6138	296	7	,	,	PUNCT
ejpam-6138	296	8	a.	a.	PROPN
ejpam-6138	296	9	zada	zada	PROPN
ejpam-6138	296	10	,	,	PUNCT
ejpam-6138	296	11	i.	i.	PROPN
ejpam-6138	296	12	l.	l.	PROPN
ejpam-6138	296	13	popa	popa	PROPN
ejpam-6138	296	14	,	,	PUNCT
ejpam-6138	296	15	and	and	CCONJ
ejpam-6138	296	16	m.	m.	PROPN
ejpam-6138	296	17	e.	e.	PROPN
ejpam-6138	296	18	samei	samei	PROPN
ejpam-6138	296	19	.	.	PUNCT
ejpam-6138	297	1	existence	existence	NOUN
ejpam-6138	297	2	and	and	CCONJ
ejpam-6138	297	3	stability	stability	NOUN
ejpam-6138	297	4	of	of	ADP
ejpam-6138	297	5	a	a	DET
ejpam-6138	297	6	qcaputo	qcaputo	NOUN
ejpam-6138	297	7	fractional	fractional	ADJ
ejpam-6138	297	8	jerk	jerk	NOUN
ejpam-6138	297	9	differential	differential	NOUN
ejpam-6138	297	10	equation	equation	NOUN
ejpam-6138	297	11	having	have	VERB
ejpam-6138	297	12	anti	anti	ADJ
ejpam-6138	297	13	-	-	ADJ
ejpam-6138	297	14	periodic	periodic	ADJ
ejpam-6138	297	15	boundary	boundary	ADJ
ejpam-6138	297	16	conditions	condition	NOUN
ejpam-6138	297	17	.	.	PUNCT
ejpam-6138	298	1	boundary	boundary	ADJ
ejpam-6138	298	2	value	value	NOUN
ejpam-6138	298	3	problems	problem	NOUN
ejpam-6138	298	4	,	,	PUNCT
ejpam-6138	298	5	2024:28	2024:28	NUM
ejpam-6138	298	6	,	,	PUNCT
ejpam-6138	298	7	2024	2024	NUM
ejpam-6138	298	8	.	.	PUNCT
ejpam-6138	299	1	[	[	X
ejpam-6138	299	2	3	3	NUM
ejpam-6138	299	3	]	]	X
ejpam-6138	299	4	n.	n.	PROPN
ejpam-6138	299	5	mehmood	mehmood	PROPN
ejpam-6138	299	6	,	,	PUNCT
ejpam-6138	299	7	a.	a.	NOUN
ejpam-6138	299	8	m.	m.	PROPN
ejpam-6138	299	9	z.	z.	PROPN
ejpam-6138	299	10	nisar	nisar	PROPN
ejpam-6138	299	11	,	,	PUNCT
ejpam-6138	299	12	and	and	CCONJ
ejpam-6138	299	13	t.	t.	PROPN
ejpam-6138	299	14	abdeljawad	abdeljawad	NOUN
ejpam-6138	299	15	.	.	PUNCT
ejpam-6138	300	1	analysis	analysis	NOUN
ejpam-6138	300	2	of	of	ADP
ejpam-6138	300	3	js	js	ADJ
ejpam-6138	300	4	-	-	PUNCT
ejpam-6138	300	5	contractions	contraction	NOUN
ejpam-6138	300	6	with	with	ADP
ejpam-6138	300	7	applications	application	NOUN
ejpam-6138	300	8	to	to	ADP
ejpam-6138	300	9	fractional	fractional	ADJ
ejpam-6138	300	10	boundary	boundary	ADJ
ejpam-6138	300	11	value	value	NOUN
ejpam-6138	300	12	problems	problem	NOUN
ejpam-6138	300	13	.	.	PUNCT
ejpam-6138	301	1	journal	journal	PROPN
ejpam-6138	301	2	of	of	ADP
ejpam-6138	301	3	inequalities	inequality	NOUN
ejpam-6138	301	4	and	and	CCONJ
ejpam-6138	301	5	applications	application	NOUN
ejpam-6138	301	6	,	,	PUNCT
ejpam-6138	301	7	2021:93	2021:93	NUM
ejpam-6138	301	8	,	,	PUNCT
ejpam-6138	301	9	2021	2021	NUM
ejpam-6138	301	10	.	.	PUNCT
ejpam-6138	302	1	[	[	X
ejpam-6138	302	2	4	4	X
ejpam-6138	302	3	]	]	PUNCT
ejpam-6138	302	4	s.	s.	PROPN
ejpam-6138	302	5	p.	p.	PROPN
ejpam-6138	302	6	bhairat	bhairat	PROPN
ejpam-6138	302	7	and	and	CCONJ
ejpam-6138	302	8	m.	m.	PROPN
ejpam-6138	302	9	e.	e.	PROPN
ejpam-6138	302	10	samei	samei	PROPN
ejpam-6138	302	11	.	.	PUNCT
ejpam-6138	303	1	non	non	ADJ
ejpam-6138	303	2	-	-	NOUN
ejpam-6138	303	3	existence	existence	NOUN
ejpam-6138	303	4	of	of	ADP
ejpam-6138	303	5	a	a	DET
ejpam-6138	303	6	global	global	ADJ
ejpam-6138	303	7	solution	solution	NOUN
ejpam-6138	303	8	for	for	ADP
ejpam-6138	303	9	hilferkatugampola	hilferkatugampola	PROPN
ejpam-6138	303	10	fractional	fractional	PROPN
ejpam-6138	303	11	differential	differential	NOUN
ejpam-6138	303	12	problem	problem	NOUN
ejpam-6138	303	13	.	.	PUNCT
ejpam-6138	304	1	partial	partial	ADJ
ejpam-6138	304	2	differential	differential	ADJ
ejpam-6138	304	3	equations	equation	NOUN
ejpam-6138	304	4	in	in	ADP
ejpam-6138	304	5	applied	applied	ADJ
ejpam-6138	304	6	mathematics	mathematic	NOUN
ejpam-6138	304	7	,	,	PUNCT
ejpam-6138	304	8	7:100495	7:100495	NUM
ejpam-6138	304	9	,	,	PUNCT
ejpam-6138	304	10	2023	2023	NUM
ejpam-6138	304	11	.	.	PUNCT
ejpam-6138	305	1	z.	z.	PROPN
ejpam-6138	305	2	bekri	bekri	PROPN
ejpam-6138	305	3	et	et	PROPN
ejpam-6138	305	4	al	al	PROPN
ejpam-6138	305	5	.	.	PUNCT
ejpam-6138	305	6	/	/	SYM
ejpam-6138	305	7	eur	eur	PROPN
ejpam-6138	305	8	.	.	PUNCT
ejpam-6138	306	1	j.	j.	PROPN
ejpam-6138	306	2	pure	pure	PROPN
ejpam-6138	306	3	appl	appl	PROPN
ejpam-6138	306	4	.	.	PROPN
ejpam-6138	306	5	math	math	PROPN
ejpam-6138	306	6	,	,	PUNCT
ejpam-6138	306	7	18	18	NUM
ejpam-6138	306	8	(	(	PUNCT
ejpam-6138	306	9	2	2	NUM
ejpam-6138	306	10	)	)	PUNCT
ejpam-6138	306	11	(	(	PUNCT
ejpam-6138	306	12	2025	2025	NUM
ejpam-6138	306	13	)	)	PUNCT
ejpam-6138	306	14	,	,	PUNCT
ejpam-6138	306	15	6138	6138	NUM
ejpam-6138	306	16	16	16	NUM
ejpam-6138	306	17	of	of	ADP
ejpam-6138	306	18	17	17	NUM
ejpam-6138	306	19	[	[	SYM
ejpam-6138	306	20	5	5	NUM
ejpam-6138	306	21	]	]	PUNCT
ejpam-6138	306	22	a.	a.	NOUN
ejpam-6138	306	23	berhail	berhail	PROPN
ejpam-6138	306	24	,	,	PUNCT
ejpam-6138	306	25	n.	n.	PROPN
ejpam-6138	306	26	tabouche	tabouche	PROPN
ejpam-6138	306	27	,	,	PUNCT
ejpam-6138	306	28	j.	j.	PROPN
ejpam-6138	306	29	alzabut	alzabut	PROPN
ejpam-6138	306	30	,	,	PUNCT
ejpam-6138	306	31	and	and	CCONJ
ejpam-6138	306	32	m.	m.	PROPN
ejpam-6138	306	33	e.	e.	PROPN
ejpam-6138	306	34	samei	samei	PROPN
ejpam-6138	306	35	.	.	PUNCT
ejpam-6138	307	1	using	use	VERB
ejpam-6138	307	2	hilfer	hilfer	NOUN
ejpam-6138	307	3	-	-	PUNCT
ejpam-6138	307	4	katugampola	katugampola	NOUN
ejpam-6138	307	5	fractional	fractional	ADJ
ejpam-6138	307	6	derivative	derivative	NOUN
ejpam-6138	307	7	in	in	ADP
ejpam-6138	307	8	initial	initial	ADJ
ejpam-6138	307	9	value	value	NOUN
ejpam-6138	307	10	mathieu	mathieu	PROPN
ejpam-6138	307	11	fractional	fractional	ADJ
ejpam-6138	307	12	differential	differential	ADJ
ejpam-6138	307	13	equations	equation	NOUN
ejpam-6138	307	14	with	with	ADP
ejpam-6138	307	15	application	application	NOUN
ejpam-6138	307	16	on	on	ADP
ejpam-6138	307	17	particle	particle	NOUN
ejpam-6138	307	18	in	in	ADP
ejpam-6138	307	19	the	the	DET
ejpam-6138	307	20	plane	plane	NOUN
ejpam-6138	307	21	.	.	PUNCT
ejpam-6138	308	1	advances	advance	NOUN
ejpam-6138	308	2	in	in	ADP
ejpam-6138	308	3	continuous	continuous	ADJ
ejpam-6138	308	4	and	and	CCONJ
ejpam-6138	308	5	discrete	discrete	ADJ
ejpam-6138	308	6	models	model	NOUN
ejpam-6138	308	7	,	,	PUNCT
ejpam-6138	308	8	2022:44	2022:44	NUM
ejpam-6138	308	9	,	,	PUNCT
ejpam-6138	308	10	2022	2022	NUM
ejpam-6138	308	11	.	.	PUNCT
ejpam-6138	309	1	[	[	X
ejpam-6138	309	2	6	6	NUM
ejpam-6138	309	3	]	]	PUNCT
ejpam-6138	309	4	a.	a.	NOUN
ejpam-6138	309	5	khan	khan	PROPN
ejpam-6138	309	6	,	,	PUNCT
ejpam-6138	309	7	j.	j.	PROPN
ejpam-6138	309	8	f.	f.	PROPN
ejpam-6138	309	9	aguilar	aguilar	PROPN
ejpam-6138	309	10	,	,	PUNCT
ejpam-6138	309	11	t.	t.	NOUN
ejpam-6138	309	12	abdeljawad	abdeljawad	NOUN
ejpam-6138	309	13	,	,	PUNCT
ejpam-6138	309	14	and	and	CCONJ
ejpam-6138	309	15	h.	h.	PROPN
ejpam-6138	309	16	khan	khan	PROPN
ejpam-6138	309	17	.	.	PUNCT
ejpam-6138	310	1	stability	stability	NOUN
ejpam-6138	310	2	and	and	CCONJ
ejpam-6138	310	3	numerical	numerical	PROPN
ejpam-6138	310	4	simulation	simulation	NOUN
ejpam-6138	310	5	of	of	ADP
ejpam-6138	310	6	fractional	fractional	ADJ
ejpam-6138	310	7	order	order	NOUN
ejpam-6138	310	8	plant	plant	NOUN
ejpam-6138	310	9	nectar	nectar	NOUN
ejpam-6138	310	10	pollinator	pollinator	NOUN
ejpam-6138	310	11	model	model	NOUN
ejpam-6138	310	12	.	.	PUNCT
ejpam-6138	311	1	alexandria	alexandria	PROPN
ejpam-6138	311	2	engineering	engineering	PROPN
ejpam-6138	311	3	journal	journal	PROPN
ejpam-6138	311	4	,	,	PUNCT
ejpam-6138	311	5	59(1):49–59	59(1):49–59	NUM
ejpam-6138	311	6	,	,	PUNCT
ejpam-6138	311	7	2020	2020	NUM
ejpam-6138	311	8	.	.	PUNCT
ejpam-6138	312	1	[	[	X
ejpam-6138	312	2	7	7	X
ejpam-6138	312	3	]	]	PUNCT
ejpam-6138	312	4	s.	s.	PROPN
ejpam-6138	312	5	t.	t.	PROPN
ejpam-6138	312	6	m.	m.	PROPN
ejpam-6138	312	7	thabet	thabet	PROPN
ejpam-6138	312	8	,	,	PUNCT
ejpam-6138	312	9	m.	m.	NOUN
ejpam-6138	312	10	vivas	vivas	PROPN
ejpam-6138	312	11	-	-	PROPN
ejpam-6138	312	12	cortez	cortez	PROPN
ejpam-6138	312	13	,	,	PUNCT
ejpam-6138	312	14	i.	i.	PROPN
ejpam-6138	312	15	kedim	kedim	PROPN
ejpam-6138	312	16	,	,	PUNCT
ejpam-6138	312	17	m.	m.	PROPN
ejpam-6138	312	18	e.	e.	PROPN
ejpam-6138	312	19	samei	samei	PROPN
ejpam-6138	312	20	,	,	PUNCT
ejpam-6138	312	21	and	and	CCONJ
ejpam-6138	312	22	m.	m.	PROPN
ejpam-6138	312	23	i.	i.	PROPN
ejpam-6138	312	24	ayari	ayari	PROPN
ejpam-6138	312	25	.	.	PUNCT
ejpam-6138	313	1	solvability	solvability	NOUN
ejpam-6138	313	2	of	of	ADP
ejpam-6138	313	3	ϱ-hilfer	ϱ-hilfer	PRON
ejpam-6138	313	4	fractional	fractional	ADJ
ejpam-6138	313	5	snap	snap	ADJ
ejpam-6138	313	6	dynamic	dynamic	ADJ
ejpam-6138	313	7	system	system	NOUN
ejpam-6138	313	8	on	on	ADP
ejpam-6138	313	9	unbounded	unbounded	ADJ
ejpam-6138	313	10	domains	domain	NOUN
ejpam-6138	313	11	.	.	PUNCT
ejpam-6138	314	1	fractal	fractal	PROPN
ejpam-6138	314	2	and	and	CCONJ
ejpam-6138	314	3	fractional	fractional	ADJ
ejpam-6138	314	4	,	,	PUNCT
ejpam-6138	314	5	7(8):607	7(8):607	NUM
ejpam-6138	314	6	,	,	PUNCT
ejpam-6138	314	7	2023	2023	NUM
ejpam-6138	314	8	.	.	PUNCT
ejpam-6138	315	1	[	[	X
ejpam-6138	315	2	8	8	NUM
ejpam-6138	315	3	]	]	PUNCT
ejpam-6138	315	4	s.	s.	PROPN
ejpam-6138	315	5	naz	naz	PROPN
ejpam-6138	315	6	and	and	CCONJ
ejpam-6138	315	7	m.	m.	PROPN
ejpam-6138	315	8	n.	n.	PROPN
ejpam-6138	315	9	naeem	naeem	PROPN
ejpam-6138	315	10	.	.	PUNCT
ejpam-6138	316	1	on	on	ADP
ejpam-6138	316	2	the	the	DET
ejpam-6138	316	3	generalization	generalization	NOUN
ejpam-6138	316	4	of	of	ADP
ejpam-6138	316	5	k	k	ADJ
ejpam-6138	316	6	-	-	PUNCT
ejpam-6138	316	7	fractional	fractional	ADJ
ejpam-6138	316	8	hilfer	hilfer	NOUN
ejpam-6138	316	9	-	-	PUNCT
ejpam-6138	316	10	katugampola	katugampola	NOUN
ejpam-6138	316	11	derivative	derivative	NOUN
ejpam-6138	316	12	with	with	ADP
ejpam-6138	316	13	cauchy	cauchy	PROPN
ejpam-6138	316	14	problem	problem	NOUN
ejpam-6138	316	15	.	.	PUNCT
ejpam-6138	317	1	turkish	turkish	ADJ
ejpam-6138	317	2	journal	journal	NOUN
ejpam-6138	317	3	of	of	ADP
ejpam-6138	317	4	mathematics	mathematic	NOUN
ejpam-6138	317	5	,	,	PUNCT
ejpam-6138	317	6	45(1):110–124	45(1):110–124	PROPN
ejpam-6138	317	7	,	,	PUNCT
ejpam-6138	317	8	2021	2021	NUM
ejpam-6138	317	9	.	.	PUNCT
ejpam-6138	318	1	[	[	X
ejpam-6138	318	2	9	9	NUM
ejpam-6138	318	3	]	]	PUNCT
ejpam-6138	318	4	s.	s.	PROPN
ejpam-6138	318	5	naz	naz	PROPN
ejpam-6138	318	6	and	and	CCONJ
ejpam-6138	318	7	m.	m.	PROPN
ejpam-6138	318	8	n.	n.	PROPN
ejpam-6138	318	9	naeem	naeem	PROPN
ejpam-6138	318	10	.	.	PUNCT
ejpam-6138	319	1	new	new	ADJ
ejpam-6138	319	2	generalized	generalized	ADJ
ejpam-6138	319	3	reverse	reverse	ADJ
ejpam-6138	319	4	minkowski	minkowski	ADJ
ejpam-6138	319	5	inequality	inequality	NOUN
ejpam-6138	319	6	and	and	CCONJ
ejpam-6138	319	7	related	relate	VERB
ejpam-6138	319	8	integral	integral	ADJ
ejpam-6138	319	9	inequalities	inequality	NOUN
ejpam-6138	319	10	via	via	ADP
ejpam-6138	319	11	generalized	generalized	ADJ
ejpam-6138	319	12	k	k	ADJ
ejpam-6138	319	13	-	-	ADJ
ejpam-6138	319	14	fractional	fractional	ADJ
ejpam-6138	319	15	hilfer	hilfer	NOUN
ejpam-6138	319	16	-	-	PUNCT
ejpam-6138	319	17	katugampola	katugampola	NOUN
ejpam-6138	319	18	derivative	derivative	NOUN
ejpam-6138	319	19	.	.	PUNCT
ejpam-6138	320	1	punjab	punjab	PROPN
ejpam-6138	320	2	university	university	PROPN
ejpam-6138	320	3	journal	journal	NOUN
ejpam-6138	320	4	of	of	ADP
ejpam-6138	320	5	mathematics	mathematic	NOUN
ejpam-6138	320	6	,	,	PUNCT
ejpam-6138	320	7	53(4):277–293	53(4):277–293	NUM
ejpam-6138	320	8	,	,	PUNCT
ejpam-6138	320	9	2021	2021	NUM
ejpam-6138	320	10	.	.	PUNCT
ejpam-6138	321	1	[	[	X
ejpam-6138	321	2	10	10	NUM
ejpam-6138	321	3	]	]	PUNCT
ejpam-6138	321	4	s.	s.	PROPN
ejpam-6138	321	5	naz	naz	PROPN
ejpam-6138	321	6	,	,	PUNCT
ejpam-6138	321	7	m.	m.	NOUN
ejpam-6138	321	8	n.	n.	PROPN
ejpam-6138	321	9	naeem	naeem	PROPN
ejpam-6138	321	10	,	,	PUNCT
ejpam-6138	321	11	and	and	CCONJ
ejpam-6138	321	12	y.	y.	PROPN
ejpam-6138	321	13	m.	m.	PROPN
ejpam-6138	321	14	chu	chu	PROPN
ejpam-6138	321	15	.	.	PUNCT
ejpam-6138	322	1	some	some	DET
ejpam-6138	322	2	k	k	ADJ
ejpam-6138	322	3	-	-	PUNCT
ejpam-6138	322	4	fractional	fractional	ADJ
ejpam-6138	322	5	extension	extension	NOUN
ejpam-6138	322	6	of	of	ADP
ejpam-6138	322	7	grüss	grüss	NOUN
ejpam-6138	322	8	-	-	PUNCT
ejpam-6138	322	9	type	type	NOUN
ejpam-6138	322	10	inequalities	inequality	NOUN
ejpam-6138	322	11	via	via	ADP
ejpam-6138	322	12	generalized	generalized	ADJ
ejpam-6138	322	13	hilfer	hilfer	NOUN
ejpam-6138	322	14	-	-	PUNCT
ejpam-6138	322	15	katugampola	katugampola	NOUN
ejpam-6138	322	16	derivative	derivative	NOUN
ejpam-6138	322	17	.	.	PUNCT
ejpam-6138	323	1	advances	advance	NOUN
ejpam-6138	323	2	in	in	ADP
ejpam-6138	323	3	difference	difference	NOUN
ejpam-6138	323	4	equations	equation	NOUN
ejpam-6138	323	5	,	,	PUNCT
ejpam-6138	323	6	2021:6	2021:6	NUM
ejpam-6138	323	7	,	,	PUNCT
ejpam-6138	323	8	2021	2021	NUM
ejpam-6138	323	9	.	.	PUNCT
ejpam-6138	324	1	[	[	X
ejpam-6138	324	2	11	11	NUM
ejpam-6138	324	3	]	]	PUNCT
ejpam-6138	324	4	s.	s.	PROPN
ejpam-6138	324	5	naz	naz	PROPN
ejpam-6138	324	6	,	,	PUNCT
ejpam-6138	324	7	m.	m.	NOUN
ejpam-6138	324	8	n.	n.	PROPN
ejpam-6138	324	9	naeem	naeem	PROPN
ejpam-6138	324	10	,	,	PUNCT
ejpam-6138	324	11	and	and	CCONJ
ejpam-6138	324	12	y.	y.	PROPN
ejpam-6138	324	13	m.	m.	PROPN
ejpam-6138	324	14	chu	chu	PROPN
ejpam-6138	324	15	.	.	PUNCT
ejpam-6138	324	16	ostrowski	ostrowski	ADJ
ejpam-6138	324	17	-	-	PUNCT
ejpam-6138	324	18	type	type	NOUN
ejpam-6138	324	19	inequalities	inequality	NOUN
ejpam-6138	324	20	for	for	ADP
ejpam-6138	324	21	n	n	CCONJ
ejpam-6138	324	22	-	-	PUNCT
ejpam-6138	324	23	polynomial	polynomial	ADJ
ejpam-6138	324	24	p	p	NOUN
ejpam-6138	324	25	-	-	PUNCT
ejpam-6138	324	26	convex	convex	NOUN
ejpam-6138	324	27	function	function	NOUN
ejpam-6138	324	28	for	for	ADP
ejpam-6138	324	29	k	k	ADJ
ejpam-6138	324	30	-	-	PUNCT
ejpam-6138	324	31	fractional	fractional	ADJ
ejpam-6138	324	32	hilfer	hilfer	NOUN
ejpam-6138	324	33	-	-	PUNCT
ejpam-6138	324	34	katugampola	katugampola	NOUN
ejpam-6138	324	35	derivative	derivative	NOUN
ejpam-6138	324	36	.	.	PUNCT
ejpam-6138	325	1	journal	journal	PROPN
ejpam-6138	325	2	of	of	ADP
ejpam-6138	325	3	inequalities	inequality	NOUN
ejpam-6138	325	4	and	and	CCONJ
ejpam-6138	325	5	applications	application	NOUN
ejpam-6138	325	6	,	,	PUNCT
ejpam-6138	325	7	2021:117	2021:117	NUM
ejpam-6138	325	8	,	,	PUNCT
ejpam-6138	325	9	2021	2021	NUM
ejpam-6138	325	10	.	.	PUNCT
ejpam-6138	326	1	[	[	X
ejpam-6138	326	2	12	12	NUM
ejpam-6138	326	3	]	]	PUNCT
ejpam-6138	326	4	s.	s.	PROPN
ejpam-6138	326	5	naz	naz	PROPN
ejpam-6138	326	6	and	and	CCONJ
ejpam-6138	326	7	y.	y.	PROPN
ejpam-6138	326	8	m.	m.	PROPN
ejpam-6138	326	9	chu	chu	PROPN
ejpam-6138	326	10	.	.	PUNCT
ejpam-6138	327	1	a	a	DET
ejpam-6138	327	2	unified	unified	ADJ
ejpam-6138	327	3	approach	approach	NOUN
ejpam-6138	327	4	for	for	ADP
ejpam-6138	327	5	novel	novel	ADJ
ejpam-6138	327	6	estimates	estimate	NOUN
ejpam-6138	327	7	of	of	ADP
ejpam-6138	327	8	inequalities	inequality	NOUN
ejpam-6138	327	9	via	via	ADP
ejpam-6138	327	10	discrete	discrete	ADJ
ejpam-6138	327	11	fractional	fractional	ADJ
ejpam-6138	327	12	calculus	calculus	NOUN
ejpam-6138	327	13	techniques	technique	NOUN
ejpam-6138	327	14	.	.	PUNCT
ejpam-6138	328	1	alexandria	alexandria	PROPN
ejpam-6138	328	2	engineering	engineering	PROPN
ejpam-6138	328	3	journal	journal	PROPN
ejpam-6138	328	4	,	,	PUNCT
ejpam-6138	328	5	61(1):847	61(1):847	PROPN
ejpam-6138	328	6	–	–	PUNCT
ejpam-6138	328	7	854	854	NUM
ejpam-6138	328	8	,	,	PUNCT
ejpam-6138	328	9	2022	2022	NUM
ejpam-6138	328	10	.	.	PUNCT
ejpam-6138	329	1	[	[	X
ejpam-6138	329	2	13	13	NUM
ejpam-6138	329	3	]	]	X
ejpam-6138	329	4	w.	w.	PROPN
ejpam-6138	329	5	g.	g.	PROPN
ejpam-6138	329	6	kelley	kelley	PROPN
ejpam-6138	329	7	and	and	CCONJ
ejpam-6138	329	8	a.	a.	PROPN
ejpam-6138	329	9	c.	c.	PROPN
ejpam-6138	329	10	peterson	peterson	PROPN
ejpam-6138	329	11	.	.	PUNCT
ejpam-6138	330	1	the	the	DET
ejpam-6138	330	2	theory	theory	NOUN
ejpam-6138	330	3	of	of	ADP
ejpam-6138	330	4	differential	differential	ADJ
ejpam-6138	330	5	equations	equation	NOUN
ejpam-6138	330	6	.	.	PUNCT
ejpam-6138	331	1	springer	springer	NOUN
ejpam-6138	331	2	,	,	PUNCT
ejpam-6138	331	3	new	new	PROPN
ejpam-6138	331	4	york	york	PROPN
ejpam-6138	331	5	,	,	PUNCT
ejpam-6138	331	6	2010	2010	NUM
ejpam-6138	331	7	.	.	PUNCT
ejpam-6138	332	1	[	[	X
ejpam-6138	332	2	14	14	NUM
ejpam-6138	332	3	]	]	PUNCT
ejpam-6138	332	4	p.	p.	PROPN
ejpam-6138	332	5	b.	b.	PROPN
ejpam-6138	332	6	bailey	bailey	PROPN
ejpam-6138	332	7	,	,	PUNCT
ejpam-6138	332	8	l.	l.	PROPN
ejpam-6138	332	9	f.	f.	PROPN
ejpam-6138	332	10	shampine	shampine	PROPN
ejpam-6138	332	11	,	,	PUNCT
ejpam-6138	332	12	and	and	CCONJ
ejpam-6138	332	13	p.	p.	PROPN
ejpam-6138	332	14	e.	e.	PROPN
ejpam-6138	332	15	waltman	waltman	PROPN
ejpam-6138	332	16	.	.	PUNCT
ejpam-6138	333	1	nonlinear	nonlinear	ADJ
ejpam-6138	333	2	two	two	NUM
ejpam-6138	333	3	-	-	PUNCT
ejpam-6138	333	4	point	point	NOUN
ejpam-6138	333	5	boundary	boundary	ADJ
ejpam-6138	333	6	value	value	NOUN
ejpam-6138	333	7	problem	problem	NOUN
ejpam-6138	333	8	.	.	PUNCT
ejpam-6138	334	1	academic	academic	ADJ
ejpam-6138	334	2	press	press	NOUN
ejpam-6138	334	3	,	,	PUNCT
ejpam-6138	334	4	new	new	PROPN
ejpam-6138	334	5	york	york	PROPN
ejpam-6138	334	6	,	,	PUNCT
ejpam-6138	334	7	1968	1968	NUM
ejpam-6138	334	8	.	.	PUNCT
ejpam-6138	335	1	[	[	X
ejpam-6138	335	2	15	15	NUM
ejpam-6138	335	3	]	]	X
ejpam-6138	335	4	r.	r.	PROPN
ejpam-6138	335	5	p.	p.	PROPN
ejpam-6138	335	6	agarwal	agarwal	PROPN
ejpam-6138	335	7	and	and	CCONJ
ejpam-6138	335	8	d.	d.	PROPN
ejpam-6138	335	9	o’regan	o’regan	PROPN
ejpam-6138	335	10	.	.	PUNCT
ejpam-6138	336	1	an	an	DET
ejpam-6138	336	2	introduction	introduction	NOUN
ejpam-6138	336	3	to	to	ADP
ejpam-6138	336	4	ordinary	ordinary	ADJ
ejpam-6138	336	5	differential	differential	ADJ
ejpam-6138	336	6	equations	equation	NOUN
ejpam-6138	336	7	.	.	PUNCT
ejpam-6138	337	1	springer	springer	NOUN
ejpam-6138	337	2	,	,	PUNCT
ejpam-6138	337	3	new	new	PROPN
ejpam-6138	337	4	york	york	PROPN
ejpam-6138	337	5	,	,	PUNCT
ejpam-6138	337	6	2008	2008	NUM
ejpam-6138	337	7	.	.	PUNCT
ejpam-6138	338	1	[	[	X
ejpam-6138	338	2	16	16	NUM
ejpam-6138	338	3	]	]	PUNCT
ejpam-6138	338	4	a.	a.	NOUN
ejpam-6138	338	5	a.	a.	NOUN
ejpam-6138	338	6	kilbas	kilbas	PROPN
ejpam-6138	338	7	,	,	PUNCT
ejpam-6138	338	8	h.	h.	PROPN
ejpam-6138	338	9	m.	m.	PROPN
ejpam-6138	338	10	srivastava	srivastava	PROPN
ejpam-6138	338	11	,	,	PUNCT
ejpam-6138	338	12	and	and	CCONJ
ejpam-6138	338	13	j.	j.	PROPN
ejpam-6138	338	14	j.	j.	PROPN
ejpam-6138	338	15	trujillo	trujillo	PROPN
ejpam-6138	338	16	.	.	PUNCT
ejpam-6138	338	17	theory	theory	NOUN
ejpam-6138	338	18	and	and	CCONJ
ejpam-6138	338	19	applications	application	NOUN
ejpam-6138	338	20	of	of	ADP
ejpam-6138	338	21	fractional	fractional	ADJ
ejpam-6138	338	22	differential	differential	ADJ
ejpam-6138	338	23	equations	equation	NOUN
ejpam-6138	338	24	.	.	PUNCT
ejpam-6138	339	1	elsevier	elsevier	PROPN
ejpam-6138	339	2	,	,	PUNCT
ejpam-6138	339	3	new	new	PROPN
ejpam-6138	339	4	york	york	PROPN
ejpam-6138	339	5	,	,	PUNCT
ejpam-6138	339	6	2006	2006	NUM
ejpam-6138	339	7	.	.	PUNCT
ejpam-6138	340	1	[	[	X
ejpam-6138	340	2	17	17	NUM
ejpam-6138	340	3	]	]	PUNCT
ejpam-6138	340	4	z.	z.	PROPN
ejpam-6138	340	5	bekri	bekri	PROPN
ejpam-6138	340	6	,	,	PUNCT
ejpam-6138	340	7	v.	v.	PROPN
ejpam-6138	340	8	s.	s.	PROPN
ejpam-6138	340	9	erturk	erturk	PROPN
ejpam-6138	340	10	,	,	PUNCT
ejpam-6138	340	11	p.	p.	PROPN
ejpam-6138	340	12	kumar	kumar	PROPN
ejpam-6138	340	13	,	,	PUNCT
ejpam-6138	340	14	and	and	CCONJ
ejpam-6138	340	15	v.	v.	ADP
ejpam-6138	340	16	govindaraj	govindaraj	NOUN
ejpam-6138	340	17	.	.	PUNCT
ejpam-6138	341	1	some	some	DET
ejpam-6138	341	2	novel	novel	ADJ
ejpam-6138	341	3	analysis	analysis	NOUN
ejpam-6138	341	4	of	of	ADP
ejpam-6138	341	5	two	two	NUM
ejpam-6138	341	6	different	different	ADJ
ejpam-6138	341	7	caputo	caputo	PROPN
ejpam-6138	341	8	type	type	NOUN
ejpam-6138	341	9	fractional	fractional	ADJ
ejpam-6138	341	10	-	-	PUNCT
ejpam-6138	341	11	order	order	NOUN
ejpam-6138	341	12	boundary	boundary	ADJ
ejpam-6138	341	13	value	value	NOUN
ejpam-6138	341	14	problems	problem	NOUN
ejpam-6138	341	15	.	.	PUNCT
ejpam-6138	342	1	results	result	NOUN
ejpam-6138	342	2	in	in	ADP
ejpam-6138	342	3	nonlinear	nonlinear	ADJ
ejpam-6138	342	4	analysis	analysis	NOUN
ejpam-6138	342	5	,	,	PUNCT
ejpam-6138	342	6	5(3):299–311	5(3):299–311	NOUN
ejpam-6138	342	7	,	,	PUNCT
ejpam-6138	342	8	2022	2022	NUM
ejpam-6138	342	9	.	.	PUNCT
ejpam-6138	343	1	[	[	X
ejpam-6138	343	2	18	18	NUM
ejpam-6138	343	3	]	]	PUNCT
ejpam-6138	343	4	z.	z.	PROPN
ejpam-6138	343	5	bekri	bekri	PROPN
ejpam-6138	343	6	,	,	PUNCT
ejpam-6138	343	7	v.	v.	PROPN
ejpam-6138	343	8	s.	s.	PROPN
ejpam-6138	343	9	ertürk	ertürk	PROPN
ejpam-6138	343	10	,	,	PUNCT
ejpam-6138	343	11	and	and	CCONJ
ejpam-6138	343	12	p.	p.	PROPN
ejpam-6138	343	13	kumar	kumar	PROPN
ejpam-6138	343	14	.	.	PROPN
ejpam-6138	344	1	on	on	ADP
ejpam-6138	344	2	the	the	DET
ejpam-6138	344	3	existence	existence	NOUN
ejpam-6138	344	4	and	and	CCONJ
ejpam-6138	344	5	uniqueness	uniqueness	NOUN
ejpam-6138	344	6	of	of	ADP
ejpam-6138	344	7	a	a	DET
ejpam-6138	344	8	nonlinear	nonlinear	ADJ
ejpam-6138	344	9	q	q	ADJ
ejpam-6138	344	10	-	-	PUNCT
ejpam-6138	344	11	difference	difference	NOUN
ejpam-6138	344	12	boundary	boundary	ADJ
ejpam-6138	344	13	value	value	NOUN
ejpam-6138	344	14	problem	problem	NOUN
ejpam-6138	344	15	of	of	ADP
ejpam-6138	344	16	fractional	fractional	ADJ
ejpam-6138	344	17	order	order	NOUN
ejpam-6138	344	18	.	.	PUNCT
ejpam-6138	345	1	international	international	ADJ
ejpam-6138	345	2	journal	journal	NOUN
ejpam-6138	345	3	of	of	ADP
ejpam-6138	345	4	modeling	modeling	NOUN
ejpam-6138	345	5	,	,	PUNCT
ejpam-6138	345	6	simulation	simulation	NOUN
ejpam-6138	345	7	,	,	PUNCT
ejpam-6138	345	8	and	and	CCONJ
ejpam-6138	345	9	scientific	scientific	ADJ
ejpam-6138	345	10	computing	computing	NOUN
ejpam-6138	345	11	,	,	PUNCT
ejpam-6138	345	12	13(2):2250011	13(2):2250011	NUM
ejpam-6138	345	13	,	,	PUNCT
ejpam-6138	345	14	2022	2022	NUM
ejpam-6138	345	15	.	.	PUNCT
ejpam-6138	346	1	[	[	X
ejpam-6138	346	2	19	19	NUM
ejpam-6138	346	3	]	]	PUNCT
ejpam-6138	346	4	z.	z.	PROPN
ejpam-6138	346	5	bekri	bekri	PROPN
ejpam-6138	346	6	and	and	CCONJ
ejpam-6138	346	7	s.	s.	PROPN
ejpam-6138	346	8	benaicha	benaicha	PROPN
ejpam-6138	346	9	.	.	PUNCT
ejpam-6138	347	1	existence	existence	NOUN
ejpam-6138	347	2	of	of	ADP
ejpam-6138	347	3	solution	solution	NOUN
ejpam-6138	347	4	a	a	DET
ejpam-6138	347	5	fractional	fractional	ADJ
ejpam-6138	347	6	differential	differential	ADJ
ejpam-6138	347	7	equation	equation	NOUN
ejpam-6138	347	8	.	.	PUNCT
ejpam-6138	348	1	open	open	ADJ
ejpam-6138	348	2	journal	journal	PROPN
ejpam-6138	348	3	of	of	ADP
ejpam-6138	348	4	discrete	discrete	ADJ
ejpam-6138	348	5	applied	apply	VERB
ejpam-6138	348	6	mathematics	mathematic	NOUN
ejpam-6138	348	7	,	,	PUNCT
ejpam-6138	348	8	3(3):14–17	3(3):14–17	NUM
ejpam-6138	348	9	,	,	PUNCT
ejpam-6138	348	10	2020	2020	NUM
ejpam-6138	348	11	.	.	PUNCT
ejpam-6138	349	1	[	[	X
ejpam-6138	349	2	20	20	NUM
ejpam-6138	349	3	]	]	PUNCT
ejpam-6138	349	4	m.	m.	NOUN
ejpam-6138	349	5	houas	houas	NOUN
ejpam-6138	349	6	and	and	CCONJ
ejpam-6138	349	7	m.	m.	PROPN
ejpam-6138	349	8	e.	e.	PROPN
ejpam-6138	349	9	samei	samei	PROPN
ejpam-6138	349	10	.	.	PUNCT
ejpam-6138	350	1	solvability	solvability	NOUN
ejpam-6138	350	2	and	and	CCONJ
ejpam-6138	350	3	ulam	ulam	NOUN
ejpam-6138	350	4	-	-	PUNCT
ejpam-6138	350	5	hyers	hyer	NOUN
ejpam-6138	350	6	-	-	PUNCT
ejpam-6138	350	7	rassias	rassias	PROPN
ejpam-6138	350	8	stability	stability	NOUN
ejpam-6138	350	9	for	for	ADP
ejpam-6138	350	10	generalized	generalized	ADJ
ejpam-6138	350	11	sequential	sequential	ADJ
ejpam-6138	350	12	quantum	quantum	ADJ
ejpam-6138	350	13	fractional	fractional	ADJ
ejpam-6138	350	14	pantograph	pantograph	NOUN
ejpam-6138	350	15	equations	equation	NOUN
ejpam-6138	350	16	.	.	PUNCT
ejpam-6138	351	1	partial	partial	ADJ
ejpam-6138	351	2	differential	differential	PROPN
ejpam-6138	351	3	z.	z.	PROPN
ejpam-6138	351	4	bekri	bekri	PROPN
ejpam-6138	351	5	et	et	PROPN
ejpam-6138	351	6	al	al	PROPN
ejpam-6138	351	7	.	.	PUNCT
ejpam-6138	351	8	/	/	SYM
ejpam-6138	351	9	eur	eur	PROPN
ejpam-6138	351	10	.	.	PUNCT
ejpam-6138	352	1	j.	j.	PROPN
ejpam-6138	352	2	pure	pure	PROPN
ejpam-6138	352	3	appl	appl	PROPN
ejpam-6138	352	4	.	.	PROPN
ejpam-6138	352	5	math	math	PROPN
ejpam-6138	352	6	,	,	PUNCT
ejpam-6138	352	7	18	18	NUM
ejpam-6138	352	8	(	(	PUNCT
ejpam-6138	352	9	2	2	NUM
ejpam-6138	352	10	)	)	PUNCT
ejpam-6138	352	11	(	(	PUNCT
ejpam-6138	352	12	2025	2025	NUM
ejpam-6138	352	13	)	)	PUNCT
ejpam-6138	352	14	,	,	PUNCT
ejpam-6138	352	15	6138	6138	NUM
ejpam-6138	352	16	17	17	NUM
ejpam-6138	352	17	of	of	ADP
ejpam-6138	352	18	17	17	NUM
ejpam-6138	352	19	equations	equation	NOUN
ejpam-6138	352	20	in	in	ADP
ejpam-6138	352	21	applied	applied	ADJ
ejpam-6138	352	22	mathematics	mathematic	NOUN
ejpam-6138	352	23	,	,	PUNCT
ejpam-6138	352	24	9:100651	9:100651	NUM
ejpam-6138	352	25	,	,	PUNCT
ejpam-6138	352	26	2024	2024	NUM
ejpam-6138	352	27	.	.	PUNCT
ejpam-6138	353	1	[	[	X
ejpam-6138	353	2	21	21	NUM
ejpam-6138	353	3	]	]	PUNCT
ejpam-6138	353	4	m.	m.	NOUN
ejpam-6138	353	5	m.	m.	NOUN
ejpam-6138	353	6	matar	matar	PROPN
ejpam-6138	353	7	,	,	PUNCT
ejpam-6138	353	8	m.	m.	PROPN
ejpam-6138	353	9	e.	e.	PROPN
ejpam-6138	353	10	samei	samei	PROPN
ejpam-6138	353	11	,	,	PUNCT
ejpam-6138	353	12	s.	s.	PROPN
ejpam-6138	353	13	etemad	etemad	PROPN
ejpam-6138	353	14	,	,	PUNCT
ejpam-6138	353	15	a.	a.	NOUN
ejpam-6138	353	16	amara	amara	PROPN
ejpam-6138	353	17	,	,	PUNCT
ejpam-6138	353	18	s.	s.	PROPN
ejpam-6138	353	19	rezapour	rezapour	PROPN
ejpam-6138	353	20	,	,	PUNCT
ejpam-6138	353	21	and	and	CCONJ
ejpam-6138	353	22	j.	j.	PROPN
ejpam-6138	353	23	alzabut	alzabut	PROPN
ejpam-6138	353	24	.	.	PUNCT
ejpam-6138	354	1	stability	stability	NOUN
ejpam-6138	354	2	analysis	analysis	NOUN
ejpam-6138	354	3	and	and	CCONJ
ejpam-6138	354	4	existence	existence	NOUN
ejpam-6138	354	5	criteria	criterion	NOUN
ejpam-6138	354	6	with	with	ADP
ejpam-6138	354	7	numerical	numerical	ADJ
ejpam-6138	354	8	illustrations	illustration	NOUN
ejpam-6138	354	9	to	to	PART
ejpam-6138	354	10	fractional	fractional	ADJ
ejpam-6138	354	11	jerk	jerk	NOUN
ejpam-6138	354	12	differential	differential	NOUN
ejpam-6138	354	13	system	system	NOUN
ejpam-6138	354	14	involving	involve	VERB
ejpam-6138	354	15	generalized	generalize	VERB
ejpam-6138	354	16	caputo	caputo	PROPN
ejpam-6138	354	17	derivative	derivative	NOUN
ejpam-6138	354	18	.	.	PUNCT
ejpam-6138	355	1	qualitative	qualitative	ADJ
ejpam-6138	355	2	theory	theory	NOUN
ejpam-6138	355	3	of	of	ADP
ejpam-6138	355	4	dynamical	dynamical	ADJ
ejpam-6138	355	5	systems	system	NOUN
ejpam-6138	355	6	,	,	PUNCT
ejpam-6138	355	7	23(3):111	23(3):111	PROPN
ejpam-6138	355	8	,	,	PUNCT
ejpam-6138	355	9	2024	2024	NUM
ejpam-6138	355	10	.	.	PUNCT
ejpam-6138	356	1	[	[	X
ejpam-6138	356	2	22	22	NUM
ejpam-6138	356	3	]	]	PUNCT
ejpam-6138	356	4	a.	a.	NOUN
ejpam-6138	356	5	boutiara	boutiara	NOUN
ejpam-6138	356	6	,	,	PUNCT
ejpam-6138	356	7	m.	m.	NOUN
ejpam-6138	356	8	m.	m.	NOUN
ejpam-6138	356	9	matar	matar	PROPN
ejpam-6138	356	10	,	,	PUNCT
ejpam-6138	356	11	j.	j.	PROPN
ejpam-6138	356	12	alzabut	alzabut	PROPN
ejpam-6138	356	13	,	,	PUNCT
ejpam-6138	356	14	m.	m.	PROPN
ejpam-6138	356	15	e.	e.	PROPN
ejpam-6138	356	16	samei	samei	PROPN
ejpam-6138	356	17	,	,	PUNCT
ejpam-6138	356	18	and	and	CCONJ
ejpam-6138	356	19	h.	h.	PROPN
ejpam-6138	356	20	khan	khan	PROPN
ejpam-6138	356	21	.	.	PUNCT
ejpam-6138	357	1	investigation	investigation	NOUN
ejpam-6138	357	2	of	of	ADP
ejpam-6138	357	3	abc	abc	PROPN
ejpam-6138	357	4	coupled	couple	VERB
ejpam-6138	357	5	langevin	langevin	PROPN
ejpam-6138	357	6	fractional	fractional	PROPN
ejpam-6138	357	7	differential	differential	ADJ
ejpam-6138	357	8	equations	equation	NOUN
ejpam-6138	357	9	constrained	constrain	VERB
ejpam-6138	357	10	by	by	ADP
ejpam-6138	357	11	perov	perov	PROPN
ejpam-6138	357	12	’s	’s	PART
ejpam-6138	357	13	fixed	fix	VERB
ejpam-6138	357	14	point	point	NOUN
ejpam-6138	357	15	in	in	ADP
ejpam-6138	357	16	generalized	generalized	ADJ
ejpam-6138	357	17	banach	banach	NOUN
ejpam-6138	357	18	spaces	space	NOUN
ejpam-6138	357	19	.	.	PUNCT
ejpam-6138	358	1	aims	aim	VERB
ejpam-6138	358	2	mathematics	mathematic	NOUN
ejpam-6138	358	3	,	,	PUNCT
ejpam-6138	358	4	8(5):12109–12132	8(5):12109–12132	NUM
ejpam-6138	358	5	,	,	PUNCT
ejpam-6138	358	6	2023	2023	NUM
ejpam-6138	358	7	.	.	PUNCT
ejpam-6138	359	1	[	[	X
ejpam-6138	359	2	23	23	NUM
ejpam-6138	359	3	]	]	X
ejpam-6138	359	4	n.	n.	PROPN
ejpam-6138	359	5	adjimi	adjimi	PROPN
ejpam-6138	359	6	,	,	PUNCT
ejpam-6138	359	7	a.	a.	NOUN
ejpam-6138	359	8	boutiara	boutiara	NOUN
ejpam-6138	359	9	,	,	PUNCT
ejpam-6138	359	10	m.	m.	PROPN
ejpam-6138	359	11	e.	e.	PROPN
ejpam-6138	359	12	samei	samei	PROPN
ejpam-6138	359	13	,	,	PUNCT
ejpam-6138	359	14	s.	s.	PROPN
ejpam-6138	359	15	etemad	etemad	PROPN
ejpam-6138	359	16	,	,	PUNCT
ejpam-6138	359	17	and	and	CCONJ
ejpam-6138	359	18	s.	s.	PROPN
ejpam-6138	359	19	rezapour	rezapour	PROPN
ejpam-6138	359	20	.	.	PUNCT
ejpam-6138	360	1	on	on	ADP
ejpam-6138	360	2	solutions	solution	NOUN
ejpam-6138	360	3	of	of	ADP
ejpam-6138	360	4	a	a	DET
ejpam-6138	360	5	hybrid	hybrid	ADJ
ejpam-6138	360	6	generalized	generalize	VERB
ejpam-6138	360	7	caputo	caputo	NOUN
ejpam-6138	360	8	-	-	PUNCT
ejpam-6138	360	9	type	type	NOUN
ejpam-6138	360	10	problem	problem	NOUN
ejpam-6138	360	11	via	via	ADP
ejpam-6138	360	12	the	the	DET
ejpam-6138	360	13	measure	measure	NOUN
ejpam-6138	360	14	of	of	ADP
ejpam-6138	360	15	non	non	ADJ
ejpam-6138	360	16	-	-	NOUN
ejpam-6138	360	17	compactness	compactness	NOUN
ejpam-6138	360	18	in	in	ADP
ejpam-6138	360	19	the	the	DET
ejpam-6138	360	20	generalized	generalized	ADJ
ejpam-6138	360	21	version	version	NOUN
ejpam-6138	360	22	of	of	ADP
ejpam-6138	360	23	darbo	darbo	PROPN
ejpam-6138	360	24	’s	’s	PART
ejpam-6138	360	25	theorem	theorem	PROPN
ejpam-6138	360	26	.	.	PROPN
ejpam-6138	360	27	journal	journal	PROPN
ejpam-6138	360	28	of	of	ADP
ejpam-6138	360	29	inequalities	inequality	NOUN
ejpam-6138	360	30	and	and	CCONJ
ejpam-6138	360	31	applications	application	NOUN
ejpam-6138	360	32	,	,	PUNCT
ejpam-6138	360	33	2023:34	2023:34	NUM
ejpam-6138	360	34	,	,	PUNCT
ejpam-6138	360	35	2023	2023	NUM
ejpam-6138	360	36	.	.	PUNCT
ejpam-6138	361	1	[	[	X
ejpam-6138	361	2	24	24	NUM
ejpam-6138	361	3	]	]	PUNCT
ejpam-6138	361	4	z.	z.	PROPN
ejpam-6138	361	5	bekri	bekri	PROPN
ejpam-6138	361	6	,	,	PUNCT
ejpam-6138	361	7	v.	v.	PROPN
ejpam-6138	361	8	s.	s.	PROPN
ejpam-6138	361	9	erturk	erturk	PROPN
ejpam-6138	361	10	,	,	PUNCT
ejpam-6138	361	11	and	and	CCONJ
ejpam-6138	361	12	p.	p.	PROPN
ejpam-6138	361	13	kumar	kumar	PROPN
ejpam-6138	361	14	.	.	PROPN
ejpam-6138	362	1	existence	existence	NOUN
ejpam-6138	362	2	and	and	CCONJ
ejpam-6138	362	3	uniqueness	uniqueness	VERB
ejpam-6138	362	4	analysis	analysis	NOUN
ejpam-6138	362	5	for	for	ADP
ejpam-6138	362	6	the	the	DET
ejpam-6138	362	7	generalized	generalized	ADJ
ejpam-6138	362	8	caputo	caputo	NOUN
ejpam-6138	362	9	-	-	PUNCT
ejpam-6138	362	10	type	type	NOUN
ejpam-6138	362	11	fractional	fractional	ADJ
ejpam-6138	362	12	-	-	PUNCT
ejpam-6138	362	13	order	order	NOUN
ejpam-6138	362	14	boundary	boundary	ADJ
ejpam-6138	362	15	value	value	NOUN
ejpam-6138	362	16	problem	problem	NOUN
ejpam-6138	362	17	.	.	PUNCT
ejpam-6138	363	1	advanced	advanced	ADJ
ejpam-6138	363	2	studies	study	NOUN
ejpam-6138	363	3	in	in	ADP
ejpam-6138	363	4	contemporary	contemporary	ADJ
ejpam-6138	363	5	mathematics	mathematic	NOUN
ejpam-6138	363	6	,	,	PUNCT
ejpam-6138	363	7	33(2):173–179	33(2):173–179	PROPN
ejpam-6138	363	8	,	,	PUNCT
ejpam-6138	363	9	2023	2023	NUM
ejpam-6138	363	10	.	.	PUNCT
ejpam-6138	364	1	[	[	X
ejpam-6138	364	2	25	25	NUM
ejpam-6138	364	3	]	]	X
ejpam-6138	364	4	s.	s.	PROPN
ejpam-6138	364	5	lakhlifa	lakhlifa	PROPN
ejpam-6138	364	6	,	,	PUNCT
ejpam-6138	364	7	a.	a.	NOUN
ejpam-6138	364	8	sahar	sahar	PROPN
ejpam-6138	364	9	,	,	PUNCT
ejpam-6138	364	10	and	and	CCONJ
ejpam-6138	364	11	j.	j.	PROPN
ejpam-6138	364	12	fahd	fahd	PROPN
ejpam-6138	364	13	.	.	PUNCT
ejpam-6138	365	1	the	the	DET
ejpam-6138	365	2	general	general	PROPN
ejpam-6138	365	3	caputo	caputo	PROPN
ejpam-6138	365	4	-	-	PUNCT
ejpam-6138	365	5	katugampola	katugampola	PROPN
ejpam-6138	365	6	fractional	fractional	PROPN
ejpam-6138	365	7	derivative	derivative	ADJ
ejpam-6138	365	8	and	and	CCONJ
ejpam-6138	365	9	numerical	numerical	ADJ
ejpam-6138	365	10	approach	approach	NOUN
ejpam-6138	365	11	for	for	ADP
ejpam-6138	365	12	solving	solve	VERB
ejpam-6138	365	13	the	the	DET
ejpam-6138	365	14	fractional	fractional	ADJ
ejpam-6138	365	15	differential	differential	ADJ
ejpam-6138	365	16	equations	equation	NOUN
ejpam-6138	365	17	.	.	PUNCT
ejpam-6138	366	1	alexandria	alexandria	PROPN
ejpam-6138	366	2	engineering	engineering	PROPN
ejpam-6138	366	3	journal	journal	PROPN
ejpam-6138	366	4	,	,	PUNCT
ejpam-6138	366	5	121:539–557	121:539–557	NUM
ejpam-6138	366	6	,	,	PUNCT
ejpam-6138	366	7	2025	2025	NUM
ejpam-6138	366	8	.	.	PUNCT
ejpam-6138	367	1	[	[	X
ejpam-6138	367	2	26	26	NUM
ejpam-6138	367	3	]	]	X
ejpam-6138	367	4	u.	u.	PROPN
ejpam-6138	367	5	n.	n.	PROPN
ejpam-6138	367	6	katugampola	katugampola	PROPN
ejpam-6138	367	7	.	.	PUNCT
ejpam-6138	368	1	new	new	ADJ
ejpam-6138	368	2	approach	approach	NOUN
ejpam-6138	368	3	to	to	ADP
ejpam-6138	368	4	a	a	DET
ejpam-6138	368	5	generalized	generalized	ADJ
ejpam-6138	368	6	fractional	fractional	ADJ
ejpam-6138	368	7	integral	integral	ADJ
ejpam-6138	368	8	.	.	PUNCT
ejpam-6138	368	9	applied	apply	VERB
ejpam-6138	368	10	mathematics	mathematic	NOUN
ejpam-6138	368	11	and	and	CCONJ
ejpam-6138	368	12	computation	computation	NOUN
ejpam-6138	368	13	,	,	PUNCT
ejpam-6138	368	14	218(3):860–865	218(3):860–865	NUM
ejpam-6138	368	15	,	,	PUNCT
ejpam-6138	368	16	2011	2011	NUM
ejpam-6138	368	17	.	.	PUNCT
ejpam-6138	369	1	[	[	X
ejpam-6138	369	2	27	27	NUM
ejpam-6138	369	3	]	]	X
ejpam-6138	369	4	u.	u.	PROPN
ejpam-6138	369	5	n.	n.	PROPN
ejpam-6138	369	6	katugampola	katugampola	PROPN
ejpam-6138	369	7	.	.	PUNCT
ejpam-6138	370	1	a	a	DET
ejpam-6138	370	2	new	new	ADJ
ejpam-6138	370	3	approach	approach	NOUN
ejpam-6138	370	4	to	to	ADP
ejpam-6138	370	5	generalized	generalized	ADJ
ejpam-6138	370	6	fractional	fractional	ADJ
ejpam-6138	370	7	derivatives	derivative	NOUN
ejpam-6138	370	8	.	.	PUNCT
ejpam-6138	371	1	bulletin	bulletin	NOUN
ejpam-6138	371	2	of	of	ADP
ejpam-6138	371	3	mathematical	mathematical	ADJ
ejpam-6138	371	4	analysis	analysis	NOUN
ejpam-6138	371	5	and	and	CCONJ
ejpam-6138	371	6	applications	application	NOUN
ejpam-6138	371	7	,	,	PUNCT
ejpam-6138	371	8	6(4):1–15	6(4):1–15	NUM
ejpam-6138	371	9	,	,	PUNCT
ejpam-6138	371	10	2014	2014	NUM
ejpam-6138	371	11	.	.	PUNCT
ejpam-6138	372	1	[	[	X
ejpam-6138	372	2	28	28	NUM
ejpam-6138	372	3	]	]	X
ejpam-6138	372	4	u.	u.	PROPN
ejpam-6138	372	5	n.	n.	PROPN
ejpam-6138	372	6	katugampola	katugampola	PROPN
ejpam-6138	372	7	.	.	PUNCT
ejpam-6138	373	1	mellin	mellin	PROPN
ejpam-6138	373	2	transforms	transform	VERB
ejpam-6138	373	3	of	of	ADP
ejpam-6138	373	4	generalized	generalized	ADJ
ejpam-6138	373	5	fractional	fractional	ADJ
ejpam-6138	373	6	integrals	integral	NOUN
ejpam-6138	373	7	and	and	CCONJ
ejpam-6138	373	8	derivatives	derivative	NOUN
ejpam-6138	373	9	.	.	PUNCT
ejpam-6138	374	1	applied	apply	VERB
ejpam-6138	374	2	mathematics	mathematic	NOUN
ejpam-6138	374	3	and	and	CCONJ
ejpam-6138	374	4	computation	computation	NOUN
ejpam-6138	374	5	,	,	PUNCT
ejpam-6138	374	6	257:566–580	257:566–580	NUM
ejpam-6138	374	7	,	,	PUNCT
ejpam-6138	374	8	2015	2015	NUM
ejpam-6138	374	9	.	.	PUNCT
ejpam-6138	375	1	[	[	X
ejpam-6138	375	2	29	29	NUM
ejpam-6138	375	3	]	]	X
ejpam-6138	375	4	u.	u.	PROPN
ejpam-6138	375	5	n.	n.	PROPN
ejpam-6138	375	6	katugampola	katugampola	PROPN
ejpam-6138	375	7	.	.	PUNCT
ejpam-6138	376	1	existence	existence	NOUN
ejpam-6138	376	2	and	and	CCONJ
ejpam-6138	376	3	uniqueness	uniqueness	NOUN
ejpam-6138	376	4	results	result	NOUN
ejpam-6138	376	5	for	for	ADP
ejpam-6138	376	6	a	a	DET
ejpam-6138	376	7	class	class	NOUN
ejpam-6138	376	8	of	of	ADP
ejpam-6138	376	9	generalized	generalized	ADJ
ejpam-6138	376	10	fractional	fractional	ADJ
ejpam-6138	376	11	differential	differential	NOUN
ejpam-6138	376	12	equations	equation	NOUN
ejpam-6138	376	13	,	,	PUNCT
ejpam-6138	376	14	2014	2014	NUM
ejpam-6138	376	15	.	.	PUNCT